Papers

Bell and Cover showed that an investor who multiplies the initial unit of capital by an independent uniform random variable on $(0,2)$, and then uses the log-optimal portfolio, wins a head-to-head wealth comparison with probability at least one half against every independently randomized competitor. We explain very simply how this result transfers to testing by betting: for any composite null $\mathcal P$ and simple alternative $Q$, denoting $E^*$ as the corresponding numeraire e-variable, we show that $UE^*$ exceeds any other e-variable $E$ with probability at least half. Interestingly, we show that this competitive optimality result is actually equivalent to the numeraire inequality $\mathbb E_Q[E/E^*]\leq1$, and in general randomization only helps the numeraire and fails to improve the competitive advantage of an arbitrary e-variable. Under optional stopping with or without knowledge of $U$, we emphasize a key distinction between e-process validity and competitive optimality. We also show that competitive optimality comes at the price of expected log wealth and power: thresholding $UE^*$ at $1/\alpha$ has sharp size at most $\alpha/2$, but the factor of two actually disappears under optional stopping. Even after correcting for this factor of two, the test is dominated in conditional rejection probability by randomizing the testing threshold (randomized Markov's inequality). Thus, Bell-Cover randomization is optimal for a specific competitive objective, at the cost of others.

We study the classical multi-item monopoly setting with a single additive buyer and $m$ heterogeneous items whose values are independent but not necessarily identically distributed. Optimal truthful auctions may be randomized and complicated. We analyze the approximation ratios of three simple deterministic auctions: selling all items separately, selling them as a single grand bundle, and choosing the better of the two. Our technical cornerstone is a nonlinear mathematical programming formulation of the worst-case approximation ratio of selling separately, in discrete auctions where values lie in the grid $\{0,1/K,2/K,\dots ,1\}$. For two iid items, we construct novel tight Lagrangian dual certificates that determine this ratio exactly for any discretization parameter $K$. Taking $K\to\infty$, we obtain the tight bound $1+W(1/e)\approx 1.278$ in the continuous-valued setting, where $W$ denotes the Lambert-W function, closing the $[1.278,1.368]$ gap from the work of Hart and Nisan [EC'12, JET 2017]. For $m\geq2$ independent items, a different dual construction gives an upper bound on the approximation ratio of selling separately in terms of basic statistics of the item values. Combining this bound with new inequalities relating optimal revenue (REV), separate-selling revenue (SREV), and grand-bundle revenue (BREV), we derive improved guarantees for all three auctions. Most notably, we prove \[REV\leq 3 \max\{SREV,BREV\},\] improving upon the long-standing $5.2$ factor of Ma and Simchi-Levi [arXiv 2015, AISTATS'21] and the $6$ factor of Babaioff, Immorlica, Lucier and Weinberg [FOCS'14, JACM 2020]. For iid items, we also prove $REV\leq 4.18 BREV$.

We study the truthful and fair allocation of indivisible goods to $n$ strategic agents with additive valuations. Babaioff, Feige, and Manaker Morag [FOCS 2026] gave a randomized mechanism that uses only the agents' rankings of the goods, is truthful in expectation (TIE), and guarantees every agent $1/(H_{n-1}+2)=\Theta(1/\log n)$ of her maximin share (MMS) in every realized allocation, where $H_{n-1}$ is the $(n-1)$th harmonic number; this is nearly the best possible with rankings alone. They conjectured that cardinal information allows TIE mechanisms to achieve a constant ex-post MMS guarantee. We confirm this conjecture: our TIE mechanism guarantees every agent at least $1/7$ of her MMS in every realized allocation; moreover, the mechanism is ex-ante envy-free and can be implemented in polynomial time. Our mechanism has two key technical ingredients, both of which may be of independent interest. The first is a truthful fractional allocation rule specifying each agent's probability of receiving each good: it favors each agent on her top $n-1$ goods and reduces her probability of receiving a good for each other agent who also ranks it among her top $n-1$ goods. The second is the balanced edge coloring: we decompose these probabilities into equally likely matchings from agents to high-value goods, those that alone meet an agent's guarantee, and balance these matchings in a fine-grained way without changing any marginal probability, so that every agent who receives no high-value good can obtain sufficient value from the remaining goods without over-allocating any good.

We study information aggregation in the networked learning model introduced by Kearns, Roth, and Ryu (SODA 2026). There is a fixed distribution over $d$ features and a common label. Agents learn in topological order on a directed acyclic graph. Each observes a subset of the features and its parents' predictions, fits a linear predictor to minimize mean squared error, and passes only its prediction forward. The global predictor is the best linear predictor using all features. Kearns, Roth, and Ryu show that the output agent's error approaches the global predictor's error along sufficiently deep paths with suitable feature coverage, while insufficient depth can prevent aggregation even in large networks. In contrast to their main focus on a given graph and feature allocation, we consider the limits of the model under two settings. In the adaptive designer setting, a designer chooses the graph, feature allocation, and output agent knowing the distribution. In the oblivious designer setting, the designer fixes all three before an adversary chooses the distribution. Each agent observes one feature and receives predictions from a limited number of parents. We call the aggregation exact when the output agent matches the global predictor exactly. For $d\ge3$, we show that no finite depth guarantees exact aggregation for every distribution with one parent per agent, even when the designer knows the distribution. In contrast, two parents per agent suffice for exact aggregation even in the oblivious designer setting. A fixed graph, feature allocation, and output agent achieve this for every distribution at depth $O(d\log d)$. Knowing the distribution reduces the depth to $O(d)$. Both constructions use $O(d^2)$ agents, with a very large constant for two parents. We show the bounds on the depth and number of agents are all optimal up to constant factors.

We study the problem of covering binary strings of the same length, possibly with missing entries, by a fixed number of center strings, such that each input string is within a given relative distance of the closest center. The problem has applications in binary $k$-center clustering and bioinformatics, but our main motivation comes from computational social choice. In the setting of multi-issue approval voting, we consider an algorithmic question that precedes any election: how should representatives be designed so that as many voters as possible are willing to delegate? We study the problem in two dimensions, namely the number of centers and the agreement threshold, parameters that are application-specific, and provide a complete picture of its computational complexity when entries may be missing. For the special case without missing entries, we extend our hardness results to any number of centers and large values of threshold, leaving a narrow range of thresholds unresolved.

Online Resource Allocation (ORA) is a fundamental framework for sequential decision-making problems under budget constraints. Classical ORA models typically assume that resources are monotonic, meaning that selecting actions can only decrease the available budget. In this work, we study a more general setting with replenishable budgets, in which actions may either consume or replenish resources over time. This extension is necessary to capture scenarios such as inventory systems or energy markets in which capacity can be actively recovered. We develop a dual-based algorithm that recovers best-of-both-worlds guarantees for standard ORA when the replenishment factor $\beta = 0$, and improves them when $\beta > 0$. In particular, our algorithm attains $\widetilde{\mathcal O}(\sqrt{T})$ regret in the stochastic setting and $\widetilde{\mathcal O}(\sqrt{T})$ $\alpha$-regret in the adversarial setting, where $\alpha$ depends on the per-round budget and on the replenishment factor of the void action. Moreover, the algorithm ensures strict satisfaction of the budget constraints.

We study the Reverse Sequential Proportional Approval Voting Rule (RevSeqPAV) in approval-based committee elections. Despite its historical prominence and practical use, its properties and guarantees are much less understood than those of Sequential PAV. We analyze it along two dimensions: proportional representation (measured by Extended Justified Representation, its approximations, and proportionality degree) and approximation of the maximum PAV score of instances. We first establish strong negative results for general, unrestricted election instances and then identify settings in which the rule provides meaningful fairness and optimization guarantees.

We study truthful-in-expectation (TIE) mechanisms for allocating indivisible chores alongside ex-post maximin share (MMS) guarantees. For goods, Bu and Tao (FOCS 2025) established a (1/n)-approximation for TIE mechanisms, and this was substantially improved by Babaioff, Feige, and Manaker Morag (FOCS 2026), who established an \Omega(1/\log n) approximation, where n is the number of agents. The corresponding problem for chores has received less attention. The best-known result is due to Aziz, Li, and Wu (MAPR 2024), who gave a TIE mechanism with an O(\sqrt{\log n}) MMS approximation guarantee that holds only in expectation. They also established a 6/5 lower bound for TIE mechanisms for two agents. In this paper, we present the first TIE mechanism for chores that achieves a constant ex-post MMS approximation guarantee. Specifically, our mechanism guarantees an ex-post ratio of 1.97 for any number of agents n, which improves to 4/3 for n=2 and 3/2 for n=3. On the hardness side, we tighten the two-agent lower bound to 4/3, showing that our mechanism is optimal for n=2. More generally, we establish a lower bound of 13/12 on the ex-post MMS approximation ratio achievable by TIE mechanisms for every n\ge 3.

A random assignment of n indivisible objects to n agents is specified by its assignment matrix and implemented by drawing a deterministic assignment from a Birkhoff-von Neumann decomposition. Kawase et al. observed that the choice of decomposition matters for fairness: a matrix that is envy-free in the sense of stochastic dominance (SD-EF) can be decomposed so that some agent envies another with probability close to 1. They call a decomposition Dec-EF if every agent envies every other agent with probability at most 1/2, proved that every SD-EF matrix admits a Dec-EF decomposition when n <= 3 or when there are at most two distinct preferences, and left the general case open. We settle the first open case: every SD-EF matrix with four agents admits a Dec-EF decomposition. The worst case over the SD-EF polytope of a profile is attained at a vertex, and our computer-aided proof enumerates all 26,927 vertices for the 762 profiles up to symmetry in exact arithmetic and certifies each by a rational decomposition. The same method settles five agents with at most four distinct preferences and the probabilistic serial rule for all five-agent profiles, and adversarial search up to seven agents finds no counterexample. For general n, an envy-budget identity shows that 1/2 is the best possible threshold. We prove that every SD-EF matrix with at most two distinct rows admits a Dec-EF decomposition, and that the maximum-entropy decomposition is Dec-EF whenever all agents but two share a preference; the latter proof rests on a new monotonicity lemma for weighted least-squares rankings. In general, natural decompositions fail: greedy Birkhoff-von Neumann can come arbitrarily close to envy probability (n-1)/n, and maximum entropy fails at n = 4 when all preferences differ. Deciding whether an arbitrary random assignment, not necessarily SD-EF, admits a Dec-EF decomposition is strongly NP-complete.

Aviation authorities worldwide expect Advanced Air Mobility (AAM) traffic management to be decentralized among service providers, requiring AAM flights to autonomously plan trajectories by predicting other flights' control inputs rather than relying on centralized coordination. Game-theoretic approaches that formulate multi-agent collision avoidance as an exact dynamic potential game can efficiently find open-loop equilibria, but they assume that agents exactly follow their equilibrium trajectories—an unrealistic assumption given uncertainties in actuation, perception, and computation. We propose a strategically robust formulation where each agent protects against a fictitious adversary that, for each timestep, perturbs other agents' control inputs within a bounded budget to minimize distance at that timestep. We show that, under reasonable assumptions on agents' distance cost and robustness levels, the strategically robust game remains an exact dynamic potential game and admits a quasi-closed-form solution to the inner adversarial problem for linear dynamics, which limits computational overhead. Experiments with up to eight agents using logarithmic distance costs show that strategic robustness selects more robust trajectories in high-collision-risk configurations while leaving low-risk trajectories nearly unchanged, with only a modest increase in runtime.

AI advice increasingly enters human decision workflows before costly information acquisition and final action. This paper studies how such advice affects decision quality, measured by the gross utility of the final action. Advice shifts beliefs before the decision maker chooses an acquisition experiment with uniformly posterior-separable (UPS) costs. The analysis characterizes gross effects through the continuation gross value generated by net-optimal acquisition. Convexity of this value function is necessary and sufficient for every AI signal to weakly improve gross utility at every prior, while nonconvexity allows a binary signal to cause gross harm. The criterion gives tight state-space results. Every AI signal is weakly gross-improving in binary-state problems under arbitrary actions, payoffs, and UPS costs. A minimal three-state problem can generate gross harm through concentrated shutdown, where valuable acquisition stops. For classification problems with Shannon acquisition costs, the criterion becomes an active-set slope test. It guarantees weak gross improvement for homogeneous classification and all three-state weighted classification problems, while a minimal four-state failure arises from attention dilution, where acquisition shifts away from high-stake distinctions. Along a Blackwell-increasing mixture path, gross utility can first decrease and then increase. With endogenous interpretation, cheaper interpretation can reduce gross utility.

Ensuring safe software updates in safety-critical systems without interrupting operation and without provisioning and activating cold spare hardware poses a fundamental challenge due to the conflict between system availability and update execution. In this paper, we present a bounded SMT encoding for synthesizing fixed global-time update schedules for timed-games with linear update automata and a fixed number of update transitions. We model the interaction between the system and the update as a two-player timed game. Our key contribution is the synthesis of global time points that define a fixed update schedule which guarantees safe and complete deployment of the update independently of the autonomous system behavior. To this end, we reduce the scheduling problem to a reachability and safety objective and encode it as a quantified SMT problem. We demonstrate it on an example system of a trajectory planner for autonomous driving, showing that the synthesized schedule ensures safe deployment under all admissible executions.

We study Nash regret minimization in unknown finite matrix games with bandit payoff feedback and observed opponent actions. We develop Optimistic Payoff Balancing (OPB), which achieves instance-dependent $\mathcal{O}(\log^2 T)$ Nash regret against arbitrary adaptive opponents, including games with nonunique equilibria. This resolves the open problem posed by Maiti et al. (2025), extending their polylogarithmic guarantee under bandit feedback from $2\times2$ games to arbitrary finite dimensions. To handle nonunique equilibria, we construct a reference strategy that leaves room for local adjustments. We order independent payoff differences by estimation accuracy and scale these adjustments by uncertainty, allowing the learner to exploit the opponent's imbalance to offset estimation costs. Our result thus shows that observing opponent actions suffices for polylogarithmic Nash regret in general finite matrix games.

Graph Neural Networks (GNNs) are effective for learning node and link embeddings through permutation-equivariant aggregation. However, standard GNNs collapse automorphic nodes, i.e., those with identical structural roles (or orbits) into indistinguishable representations, leading to the node automorphism problem. This collapse limits their expressive power and degrades link prediction performance. Existing approaches to characterize GNN expressiveness rely primarily on Weisfeiler-Lehman (WL) analyses, but these methods are typically qualitative and often misaligned with empirical results. To address this gap, we begin by introducing a novel quantitative framework to assess GNN expressiveness for link prediction. We first formalize edge-level automorphism through edge orbits, which capture the set of structural role pairs for nodes that share a link. Then, we introduce the edge automorphism ratio (EAR), a scalar metric that quantifies a GNN's ability to distinguish links in a given graph. We empirically demonstrate that EAR correlates strongly with performance, validating its practical benefit. Building on this insight, we design EDGE-ORBIT EQUIVARIANT GRAPH NEURAL NETWORK (EO-GNN), a GNN architecture that addresses automorphism collapse while preserving equivariance and incurring minimal computational overhead. EO-GNN accomplishes this through two core designs combined with WL-based node hashes: (i) automorphism-aware dropouts and (ii) subgraph orbit-biased aggregation. Empirical evaluations on synthetic and real graphs show improvements of up to 42.36% and 28.44%, respectively, in predicting links in scenarios with high automorphism.

We study the computational complexity of optimal contract design in the multi-agent binary-action model, focusing on gross-substitutes reward functions and related classes. While additive rewards admit an FPTAS and general submodular rewards admit only constant-factor approximation, the complexity within the intermediate class of gross substitutes has remained largely open. We uncover a fine-grained approximation landscape within this class. We first show that the optimal contract problem is APX-complete even for OXS rewards - a strict subclass of gross substitutes rewards, ruling out a PTAS for gross substitutes unless $\mathsf{P}=\mathsf{NP}$. In contrast, for weighted matroid rank functions (WMRFs) - another natural subclass of gross substitutes - we obtain an EPTAS and show that no randomized FPTAS exists in general. We further identify the special case of partition (weighted) matroid rank functions, for which we obtain an FPTAS. This stands in contrast to the multi-agent multi-action setting, where no PTAS exists even for unweighted partition matroid rank functions. Finally, we consider the broader class of ultra reward functions. While ultra rewards retain the tractability of gross substitutes in a related combinatorial contract model with a single agent, we show a sharp contrast in the multi-agent model: no polynomial-time randomized algorithm using value queries can achieve a $2^{o(n)}$-approximation in expectation. Together, our results reveal several qualitatively distinct computational regimes within and beyond gross substitutes, and identify submodularity as a crucial ingredient for the approximability of multi-agent contracts.

We study last-iterate convergence in unknown two-player zero-sum matrix games with bandit payoff feedback and observed opponent actions. For games with $d$ actions per player, we develop an algorithm achieving a duality gap of $\widetilde{\mathcal{O}}(\sqrt{d/t})$ with high probability, simultaneously at every round $t$. This improves the dimension dependence of the best previously known guarantee by a factor of $d^{3/2}$. The rate matches a standard bandit lower bound, establishing minimax optimality in both the number of actions and the number of rounds, up to logarithmic factors. The algorithm is computationally efficient, requiring only $\mathcal{O}(d)$ time and memory per round. Our technical contribution is a joint design of adaptive averaging and corrected exponential weights that absorbs estimation variance, together with a potential argument that bounds phase durations.

We introduce and study Auctions with Pacing Strategies (APS) games, a full-information model in which utility-maximizing bidders compete across many simultaneous first-price auctions, each choosing a single pacing multiplier that uniformly scales their values into bids. We settle three central questions. First, we show that there are instances that admit no approximate pure Nash equilibria. Then, we prove that the problem of deciding whether an APS game admits an (approximate) equilibrium is NP-complete in general, but can be solved in polynomial time if either the number of bidders or the number of items is fixed. Finally, when an equilibrium does exist, we characterize its inefficiency exactly, showing that both the Price of Anarchy and the Price of Stability equal $\frac{e}{e-1}$.

In school choice, a lottery number is often used by the matching mechanism to break ties when there are more students who prefer the same school than the number of seats available. There has been growing theoretical and empirical interest in understanding the impact of revealing the lottery number to students. In practice, in recent years, the NYC Public Schools started revealing the lottery number to students to improve transparency. Theoretical findings from prior literature also suggest that revealing the lottery number strictly improves the number of matches under the deferred acceptance algorithm. However, these theoretical results are based on the over-simplifying assumption that all students share the same preference ranking for schools. In this work, we relax this assumption and allow students to have heterogeneous preference rankings. Under a game-theoretic model where student strategies form a Bayesian Nash equilibrium, we characterize scenarios where revealing the lottery number can either improve or worsen the matching outcome, measured by two metrics of match rate and social welfare. We further consider revealing partial information about the lottery, and demonstrate non-monotonic effects in the amount of information available to students. These results together illustrate complex tradeoffs induced by the lottery revealing policy.

A seller and a buyer with independent private values can trade only at a posted price. We determine the worst case of this mechanism exactly: the best posted price always guarantees a $\beta_*=0.738024\ldots$ fraction of first-best welfare, where $\beta_*$ is given in closed form by the root of an explicit equation, the worst-case buyer is unique up to scaling, and the worst case is never attained. This closes the gap $[0.7292,0.73805]$ left by work from SODA 2016 through two STOC 2023 papers and AAAI 2026. The proof is an explicit certificate of optimality: after one change of variables, the gap between the optimum and the value of any buyer is a sum of nonnegative integrals, as in a linear-programming dual, and equality identifies the worst-case shape. The certificate also gives the complete tradeoff between gains from trade and the seller's initial welfare: when first-best gains from trade are a fraction $\kappa$ of initial seller welfare, the exact worst-case fraction $\rho(\kappa)$ of gains obtained by the best price satisfies $\rho(\kappa)\sim2/\log(1/\kappa)$ as $\kappa\to0$. The worst-case buyer's survival function has two constant segments joined by an explicit nonexponential curve, and the worst case is approached through a vanishing atom escaping to infinity. The same constant is the exact guarantee of dominant-strategy mechanisms with individual rationality and strong budget balance in every realization. For two units with increasing submodular valuations, an explicit finite instance has ratio below $0.7290804$, so two units are strictly harder than one. Fixing the buyer, we characterize the least probability a random common price needs to guarantee a given ratio against every seller; bounding this quantity over all buyers would determine the exact two-unit constant. Within an explicit family the worst ratio is $0.729080\ldots$, conjectured to be the two-unit constant.

We study the trade-off between squared-error accuracy and incentive compatibility in linear regression. Agents report private labels associated with publicly known features and prefer predictions close to their true labels. Ordinary least squares (OLS) need not elicit truthful reports. For regression with $d$ parameters, we design a deterministic group-strategyproof mechanism achieving a $(d+1)$-approximation to the least-squares optimum and prove optimality even among universally strategyproof randomized mechanisms, answering an open question of Chen et al. (EC 2018). Relaxing universal strategyproofness to strategyproofness in expectation reveals a sharp separation: squared individual loss retains the factor $d+1$, while absolute individual loss admits the tight ratio $2-1/(\lceil d/2\rceil+1)$.

We study whether systems with multiple concurrent proposers (MCP) incentivize the geographic decentralization of proposers. In our model, concurrent proposers strategically choose their locations to maximize their captured market share of users, who decide where to send transactions by comparing each proposer's time to inclusion. The time to inclusion between a user and a proposer consists of two terms: the distance between them, and the distance between the proposer and her nearest quorum of attesters, the latter of which we term the quorum radius. We formally prove that proposers' quorum radii are the determinant of their incentives: proposers optimally choose where to locate in order to minimize their quorum radii. We obtain as a result co-location when proposers also serve as attesters, but geographic diversity when these roles are separate. We also examine pre-confirmations and faster intervalidator connections, showing that they attenuate the influence of the quorum radius and further destabilize co-location incentives.

Residual policy adaptation provides a lightweight way to modify a strong reference policy, but a shared scale and a fixed subgroup partition can hide heterogeneous degradation and become fragile when the deployment mixture of information states changes. We introduce RSD-Poker, a structure-adaptive and shift-robust certification framework that freezes a bank of residual families and scales, learns a policy-visible partition on an independent structure split, and freezes that partition before calibration labels are joined. Each candidate-group pair receives a weighted simultaneous upper certificate for anchor-relative risk and a lower certificate for weak-response utility. A robust group-to-candidate map is then selected over a predeclared uncertainty set of deployment group proportions. Under independent calibration units drawn from each frozen group's law, a candidate bank and partition fixed before calibration, and invariant within-group conditionals, the selected map satisfies its declared mixture-robust risk budget and utility certificate with probability at least $1-\zeta_{risk}-\zeta_{util}$. The information contract supports both a teacher-backed transform and a teacher-free observation-only student. The retained deterministic 24-state audit remains an exact replay diagnostic: empirical-zero selects $\alpha=0.08$, raising the weak-response proxy from 4.2082 to 4.2889 with $0/12$ held-out threshold crossings. On stratified held-out states, the learned-partition dual selector raises weak utility from 4.4074 under global dual certification to 4.4936 and lowers held-out violation from 0.0215 to 0.0078; its mixture-robust variant reaches violation 0.0059. Across five observation-only checkpoints, risk-calibrated residuals attain weak utility $4.3659\pm0.0177$ and violation rate $0.0178\pm0.0057$.

We consider allocation of indivisible goods to agents with equal entitlements and subadditive valuations. As an ex-post fairness notion we consider the maximin share (MMS), and as an ex-ante fairness notion we consider the maximum expectation share (MES), which is always at least as large as the MMS, and sometimes much larger. We present a simple transformation that for every $0 < \rho \le 1$, given any algorithm that produces $\rho$-MMS allocations, transforms it into a randomized allocation algorithm that offers $\rho$-MMS ex-post simultaneously with $\eta$-MES ex-ante. We prove several new properties of MES, and use them to show that $\eta \ge \min[\frac{\rho}{2 + \rho}, \frac{1}{4}]$. We also present cases in which the transformation results in a higher value of $\eta$. Applying our transformation to currently known allocation algorithms shows for subadditive valuations the existence of randomized allocations that are simultaneously $\Omega(\frac{1}{\log\log n})$-MES ex-ante and $\Omega(\frac{1}{\log\log n})$-MMS ex-post, and for XOS valuations the existence of randomized allocations that are simultaneously $\frac{4}{27}$-MES ex-ante and $\frac{4}{17}$-MMS ex-post.

Learning-augmented algorithms for metrical task systems (MTS) can exploit predictions of canonical dual values, but existing formulations typically require a prediction for every state. We study whether these predictions can be compressed to a small set of representative states while retaining their algorithmic value. We introduce landmark-compressed value predictions, in which the predictor reports predicted dual values only at $m$ landmarks and the remaining values are reconstructed by a Lipschitz extension. Our algorithm achieves additive excess cost $O(T\,r(L) + \sum_t \delta_t)$, where $r(L)$ is the covering radius of the landmarks and $\delta_t$ measures prediction error up to additive shifts; local and value-dependent bounds refine this guarantee. For sparse landmark sets on unit-spaced finite lines, we prove a matching $\Omega(T r_m)$ lower bound for every randomized algorithm using fixed landmarks, even with advance access to their entire exact absolute-value table. The prediction interface also matters: on two states with one landmark, exact absolute values permit horizon-independent excess, whereas exact relative values force worst-case expected excess linear in $T$. We give PAC guarantees for learning compressed prediction tables, with efficient empirical-risk minimization for fixed landmarks. Our results connect metric coverage, prediction interfaces, and learning guarantees for compressed predictions in online MTS.

Coupled rollouts can reduce the noise of counterfactual action comparisons, but two issues prevent standard common-random-number constructions from serving as a general learning primitive in imperfect-information environments. First, an invalid coupling may expose hidden state, synchronize endogenous policy randomness, or misalign chance events after counterfactual histories diverge. Second, in multi-action policy optimization, lower return-contrast variance is not by itself the relevant objective: the optimizer depends on the return covariance matrix after projection through the local policy-gradient geometry. We introduce observation-safe counterfactual coupling (OSCC), a framework that defines an admissible class through marginal preservation, information-state safety, branch-local policy randomness, semantic event alignment, and trace-before-oracle replay. We derive a gradient-aware coupling criterion showing that, for marginal-preserving couplings, policy-gradient noise changes are determined by policy-Jacobian-weighted off-diagonal return covariance. This motivates OSCC-Select, a calibration-only selector that chooses among independent, root-only, continuation-only, and fully coupled rollouts using separate safety and gain certificates. Its gain target combines projected gradient noise with measured physical sampling cost and falls back to independent sampling whenever a simultaneous lower confidence bound does not certify improvement. On 100,000 fixed-root Leduc comparisons, the fully coupled CP-GRPO instantiation reduces return-contrast variance from 41.1158 to 18.1441, a 55.87% reduction, while preserving the declared branch marginals. With three actions, OSCC-Select chooses continuation coupling and attains gradient-noise trace 0.0783 versus 0.0917 for return-variance selection. Increasing calibration from 64 to 2,048 groups raises certification from 0.327 to 0.995.

We study the problem of computing how close a given election is to being group-separable, measuring proximity by swaps of adjacent candidates in the votes. We also consider several other domains, including caterpillar group-separable, balanced group-separable, single-peaked, and single-crossing ones. Our problem is generally intractable, but we find practical FPT algorithms parameterized by the number of candidates or swaps. For the latter case, our algorithm applies to all domains characterized by finite forbidden subelections, resolving a well-established open problem. We supplement our theoretical findings with experimental analysis.

Markets for data promise to unlock its economic value, yet in practice they remain far less active than expected—one reason is that those who supply data are not rewarded for the value it creates downstream. A defining feature of data is its replicability: a buyer can refine purchased data into a new product and resell it to many downstream buyers, so a single source seeds a branching cascade of resales that naturally forms a tree. Because an upstream seller captures none of this downstream value, its incentive to trade is weakened. Existing works propose profit reallocation—returning part of downstream revenue to upstream contributors—as a natural remedy. But whether profit reallocation works on the tree-structured markets that replicable data actually induces has remained open. To bridge this gap, we develop a principled framework for profit reallocation on tree-structured data markets. We introduce a sequential trading game on a tree and a general class of budget-feasible profit reallocation mechanisms (PRMs) over it. We derive efficient algorithms to compute the induced equilibria—a polynomial-time exact algorithm for discrete valuations and a fully polynomial-time approximation scheme (FPTAS) for continuous ones—via a subtree decomposition technique that tames the potential coupling across a seller's children. We then prove that, under mild assumptions, any budget-feasible PRM weakly expands the trades that occur in equilibrium, and any budget-balanced PRM additionally weakly improves social welfare, relative to the baseline that reallocates nothing. Experiments on synthetic markets confirm that these benefits are substantial, persist even when the assumptions fail, and grow with the depth and branching of the tree.

The recent resolution of the Nisan–Ronen conjecture~\cite{NR,CKK} establishes that the optimal worst-case approximation ratio of deterministic truthful mechanisms for makespan on m unrelated machines is exactly m. We ask how prior information, Bayesian incentive compatibility (BIC), randomization, and machine-side resource augmentation change this barrier. We obtain three main results. First, we prove an asymptotic 4/3 lower bound for randomized BIC mechanisms with two machines, strengthening the previous 1.2 deterministic-BIC lower bound~\cite{MS}. Second, in the prior-free setting for two machines, randomization improves the known truthful ratio from 2 to 7/4~\cite{NR}. We show that randomized BIC scheduling mechanisms are likewise strictly more powerful than their deterministic counterparts, exhibiting an asymptotic BIC-integrality gap of 8/7. Thus, optimality in prior-dependent BIC scheduling can strictly require randomization. This parallels the role of lotteries in multidimensional revenue maximization, where randomization can strictly improve revenue~\cite{MV,BCKW}. Third, we show that when job assignments are sufficiently well spread across machines (more formally, when the pairwise collision parameter $\Delta_r$ is bounded by a constant independent of both the number of machines m and the number of sampled layers r), then $O(m/\varepsilon)$ sampled layers suffice for the standard truthful MinWork mechanism to achieve a $1+\varepsilon$-approximation to the original first-best benchmark. Equivalently, $O(m/\varepsilon)$ sampled replicas per machine suffice. This resource-augmentation result parallels the Bulow–Klemperer perspective~\cite{BK,EFFTW}. As a by-product, in the standard unaugmented model, MinWork achieves a $(1+\frac{\Delta_1(m-1)}{2})$-approximation to the first-best benchmark for every prior.

As large language models advance, AI agents are moving beyond isolated, domain-specific tasks toward long-horizon, cross-domain workflows. This transition exposes two challenges: increasing harness complexity makes manual design difficult to scale, while tighter coupling to specific domains limits the generality of a single harness. The central question thus shifts from how to engineer a stronger harness for one domain to how to autonomously construct specialized harnesses, improve them through experience, and orchestrate them across domains. We introduce Raven, The Harness of Harnesses, an open-source multi-agent ecosystem that automatically constructs and evolves modular harnesses for specific models and domains, treating each executable model–harness pair as a composable unit of intelligence. To support an All-Domain Collaboration Network, its Host Agent decomposes goals, matches subtasks to specialized agents, coordinates execution dependencies, and integrates results, while a host archive and EverOS preserve experience across tasks and Skill Forge makes that experience available as reusable procedures. Our theory establishes sufficient conditions for such composition to expand reliable task coverage beyond that of the available individual agents under a shared resource budget. On complex and long-horizon tasks, Raven significantly outperforms the state-of-the-art agent systems, pushing the frontier of composable agentic intelligence.

Moving ML-mediated decision making onto privacy-preserving clients decentralises the economic decision along with the inference. Shared budget constraints then depend on information that cannot be globally current, creating an information-structure failure that conventional pacing is not designed to solve. We study this information misalignment in an auction-logic-faithful on-device simulation with 36 campaigns and 50 devices. Accounting is in dimensionless integer score units; no currency semantics are claimed. Across 30 paired demand paths, proportional Even pacing overspends 17.77% after one tick of staleness and 1,669.31% after 50 ticks under the original 20-times budget pressure. The effect does not depend on that severe a budget: at two-times pressure, 50-tick overspend remains 106.95%. A visible-budget no-sale guard makes zero-lag compliance exact at this score-unit granularity, yet leaves 11.88% overspend at one tick because other devices' debits remain invisible. A declared bursty, heterogeneous-device sweep retains a strictly increasing mean lag curve. We derive a finite-window expected excess-debit bound under conditional charge caps and find positive paired slack in every bounded-value cell. A second, incentive misalignment arises when the ML/pacing score transformation is allowed to change payment units: 98.23% of rival auctions at one tick admit a profitable deviation. An executable implementation-level counterexample isolates the runner-up's multiplier in the winner's price. Critical-base-bid payment is per-auction DSIC conditional on current multipliers, but does not establish dynamic truthfulness and does not repair base-value ranking disagreement.