Utility Maximization

In this article, we propose an online electronic counter-countermeasure (ECCM) framework designed to conceal the strategic decision-making processes of a cognitive radar (CR) operating under adversarial surveillance. We model the CR under two distinct decision paradigms: a static constrained utility-maximizing behavior and a dynamic expected utility-maximizing behavior. The radar's utility function is modeled via a von Mises--Fisher (vMF) distribution, with the distributional parameter constituting the private information to be protected from adversarial inference. We adopt a distribution privacy framework to conceal this private information and provide formal distribution privacy guarantees for cognition masking. In this work, we develop cognition-hiding algorithms for both static constrained utility maximization (WDPCH-SU), and dynamic expected utility maximization (WDPCH-DU). Through rigorous mathematical analysis, we show that both WDPCH-SU and WDPCH-DU satisfy $ε$-distribution privacy ($ε$-DistP) against inference-based adversarial attacks and present the privacy--performance trade-off bounds, quantifying utility loss (in static setting) and expected utility deviation (in dynamic setting) as functions of $ε$. Numerical results show that WDPCH-SU gives about 15% improvement in utility loss at maximum privacy compared to the existing methodology while WDPCH-DU achieves a greater reduction in adversarial Fisher information without requiring explicit Fisher information constraints, at a moderate, analytically bounded utility deviation. These results are highly promising in many 6G communication scenarios such as network slicing for automated driving and swarm UAV coordination, where it is essential to keep the resource allocation policy robust against privacy attacks.

Coupon campaigns seek to lift both conversion and revenue, but gross merchandise value (GMV) follows a deterministic funnel from conversion to conditional order value and is zero-inflated and heavy-tailed. We propose FunnelCausalNet, an uplift estimator coupling a binary conversion head with a nonnegative conditional-value head through $μ_{\mathrm{gmv}}=μ_{\mathrm{conv}}μ_{\mathrm{val}}$. Under explicit RCT, support, rate-gap, and cross-head covariance-control assumptions, an idealized leading-order MSE comparison identifies a regime in which funnel composition can reduce pointwise variance; this is a heuristic, not a guarantee for the shared-representation neural model. The estimator is paired with marginal split-conformal CATE summaries, combined through a Bonferroni union as audit bands, and a Lagrangian budgeted allocator using RCT-anchored estimates for subsidy-aware ROI accounting. On semi-synthetic multi-tier Criteo-MT7, FunnelCausalNet's mean AUUC_GMV is within one seed standard deviation of the leading feature-interaction baseline among eleven baselines, while a controlled ablation reduces GMV effect error versus direct GMV regression by 18--48% across tested zero-inflation regimes. On de-identified industrial Hotel-Coupon RCT logs with about 4.9 million hold-out exposure records per seed, expected-outcome evaluation sweeps full LP frontiers; FunnelCausalNet has the best seed-averaged mean DeltaROI at all seven correlated anchors from 10% to 60%, which we treat as descriptive frontier consistency rather than independent significance. On sparse binary-spend public benchmarks, revenue-focused rankers can dominate uplift-curve proxies, defining an explicit regime boundary.

Incentivized advertising allocates monetary or virtual rewards to drive user engagement, where a key challenge is optimizing continuous incentive magnitudes under strict global constraints. This problem is complicated by high-frequency interactions, delayed feedback, and non-Markovian user dynamics such as fatigue, which limit the effectiveness of existing uplift modeling and constrained reinforcement learning approaches. To address these challenges, we propose GOAL, a constraint-aware generative framework that formulates incentive allocation as a conditional sequence generation problem. GOAL directly generates incentive magnitudes conditioned on user histories and system-level global pressure, and integrates a hierarchical causal state encoder to capture both local behavioral dynamics and long-range dependencies. To enable flexible constraint control, we introduce \textbf{S}afe \textbf{C}onstrained \textbf{P}olicy \textbf{O}ptimization (SCPO), which learns a single generative policy that generalizes across a spectrum of ROI constraints without retraining. Experiments on large-scale real-world data and a synthetic fatigue-aware environment show that GOAL improves long-term revenue and user retention while substantially reducing ROI violation rates compared to strong baselines.

High-resolution images and long videos provide vision-language models with rich context for multimodal reasoning and fine-grained perception, but the resulting long visual token sequences make large language model-side computation and memory costly. Existing visual token reducers often operate at prescribed rates, while recent methods adapt token counts across inputs using method-specific learned thresholds or importance predictors. We introduce RUTA, a principled Rate-Utility Token Allocation method that performs pre-LLM reduction by jointly learning which tokens to retain and how many to allocate to each image-query pair. RUTA constructs query-conditioned candidate tokens and predicts a retention probability for each candidate. During training, these probabilities parameterize independent Bernoulli gates, while their sum provides a differentiable training-time estimate of the token count for each pair. Retained tokens serve as anchors that aggregate information from non-retained tokens according to semantic affinity and spatial proximity. RUTA is optimized with a penalized rate-utility objective that balances downstream task loss against expected token usage. Averaged across five benchmarks and measured relative to each backbone's full-token baseline, RUTA uses only $2.0\%$ and $4.2\%$ of visual tokens while preserving $88.2\%$ and $94.4\%$ of task performance on LLaVA-NeXT-7B and Qwen3-VL-8B, respectively.

Social learning is a powerful mechanism through which agents learn about the world from others. However, humans sometimes choose direct experience over social learning, which can carry time and cognitive resource costs. How do people balance social and non-social learning? We propose a Rational Mentalizing model of the decision to engage in social learning. This model estimates the utility of social learning by reasoning about another agent's goal and the informativeness of their future actions. It then weighs the utility of social learning against the utility of non-social learning. Using a novel game where players choose between observing other agents or exploring the environment, we show that the Rational Mentalizing model can quantitatively capture human trade-offs between these strategies. These findings suggest that selective social learning is guided by 'Theory of Mind' in the service of utility maximization.

E-commerce platforms must allocate fixed marketing budgets across multiple channels to maximize business utility. However, standard predict-then-optimize (PTO) paradigms fail in this compositional space due to observational confounding and severe extrapolation. We formulate this challenge as a simplex-constrained uplift decision problem and propose ReAlloc, a fast-slow causal framework. Specifically, an agile Orthogonal Teacher extracts unbiased local gradients from short-term logs, while an Explanation-Guided Student distills them into a structured marginal field over long-term horizons. This design enables support-aware, conservative decisions that capture cross-channel substitutions. Extensive simulations and large-scale online A/B tests on Taobao platform demonstrate that ReAlloc achieves simultaneous lifts in both pay order and income.

We study regret minimization for learning CDF-related objectives of the form $$g(x)\cdot\mathbb{P}_{X\sim\mathcal{D}}(X\le x),$$ over $[0,1]^2$, where $g$ is a known Lipschitz function and $\mathcal{D}$ is an unknown distribution. At each round $t$, the learner selects a point $x_t$ and observes the binary feedback $\mathbb{I}(X_t\le x_t)$, where $X_t\sim\mathcal{D}$. We design an algorithm achieving regret $\widetilde{\mathcal{O}}(T^{7/10})$, improving over the previous best-known bound of $\widetilde{\mathcal{O}}(T^{3/4})$ and showing that the curse of dimensionality can be at least partially lifted for this class of objectives, though a gap remains with the $Ω(T^{2/3})$ lower bound. As an application, our techniques yield the same $\widetilde{\mathcal{O}}(T^{7/10})$ regret bound for profit maximization in repeated bilateral trade with fixed prices.

Coding agents can now be left alone to improve software against a score. In this pattern--recently popularized as "autoresearch"--the agent receives a dataset, an evaluation script, and one editable file, and iterates without supervision: modify the code, measure, keep the change if the score improves. But what does the agent actually optimize--the developer's intent, or the literal number? We ran this loop on a real production task: deciding which Quranic verses appear in a noisy speech-recognition transcript and splitting the transcript by verse. Two frontier coding agents, Claude Code and OpenAI Codex, started from the same blank file with the same instructions, budget, and reasoning effort, three runs each. Both independently invented the same algorithm (canonicalization, n-gram anchoring, dynamic-programming alignment)--and then diverged. Claude stopped early with compact, general code. Codex drove the score ~10x lower, largely by memorizing answers to individual evaluation rows (19-41 hardcoded verse ids per run): a clean natural instance of specification gaming by a production agent. In a preregistered second study, we added a held-out test set and told both agents it existed. The memorization vanished, and the score gap vanished with it--yet Codex's general core transferred better and more consistently (held-out detection+split 0.085+/-0.004 vs. 0.121+/-0.031), losing only on one missed rejection of non-recitation input. Two exploratory community arms (Cursor, Antigravity) are consistent with the pattern. Every agent's held-out solution matched or beat the hand-engineered pipeline it was built to replace--the best by an order of magnitude--and now runs in production. From the ways agents exploited our harness--reading sibling runs through shared git state, leaving notes to "future runs" in persistent memory--we distill five design rules for evaluating autonomous agents.

In this paper, we introduce Lighthouse RL, a sample-efficient reinforcement learning (RL) approach for analog circuit sizing. Traditional methods lack generalization across different performance targets, while standard RL approaches waste resources exploring unpromising regions. Our method addresses these inefficiencies through a strategic reset strategy that initializes episodes from high-performing configurations discovered during training, called "lighthouses". These states, which are closer to the target objectives, guide exploration toward promising regions. When compared to RL and Bayesian optimization methods from the literature, we demonstrate the effectiveness of our approach on a 2D benchmark problem and on two analog circuits, showing significant improvements in sample efficiency (up to 1.72x faster), optimization performance (100% vs. 0-87% success rate), generalization (75% vs. 0-50% extrapolation success), and objective maximization. This efficiency is particularly valuable for computationally expensive black-box optimization problems, and our reset strategy can be used as a plug-and-play enhancement for any RL-based optimization approach.

Attention can be viewed as an online learner over context, yet existing test-time memories cannot certify that dropping a token leaves outputs unchanged or delete its influence outright. We introduce Support Vector Attention (SV-Attention), a max-margin memory whose weights are support coefficients of a one-class SVM with fixed box parameter C. Its active-set partition gives reserve tokens exactly zero weight, certifying output-preserving eviction; a reversible incremental solver deletes a token to recover the state produced by retraining without it under the same C. In fp64 experiments, decrement and refit recover identical partitions whenever the optimum is unique, and their decision functions match to a median deviation of about 10^-9 (10^-13 on learned keys); the 10^-2 worst case is confined to ill-conditioned duplicates and remains below coefficient decay in every regime. The exact path reuses the maintained KKT inverse in a custom backward. Training uses a separate stabilized batched approximation and does not carry the exact-deletion certificate; it reaches 9,125 tokens/s on a 3.22M-parameter model, while remaining 35.8 times slower than an MPS softmax reference. At matched budgets, certified selection reaches 0.86 vs. 0.32 rare-item recall and retains 0.80 vs. 0.05 deterioration hours on real MIMIC-IV streams. We also demonstrate surgical forgetting, exact editing, patient-record deletion, and a forgettable retrieval memory over real sentence embeddings. On enwik8, the hybrid obtains 2.178 BPC vs. 2.383 for a matched-state sliding-window Transformer across seven seeds (8.6% paired improvement, p=0.001); a three-seed TinyStories result is directionally positive but not significant (p=0.057).

Pricing food products to balance profitability with consumer welfare is a central challenge for retailers. Dynamic pricing is widely used to maximize revenue, yet most pricing models optimize business objectives while overlooking consumer fairness. This paper studies the risk of consumer exploitation under dynamic food pricing in Canada and proposes a methodology that embeds fairness constraints directly into retail sales forecasting. We model total retail trade sales with a log--log Autoregressive Distributed Lag (ARDL) specification, in which the coefficient on a product price is a sales elasticity, and pose the pricing problem as maximizing forecast sales subject to price bounds anchored to the Consumer Price Index (CPI). We solve this problem with both Linear Programming (LP) and Simulated Annealing (SA), under single-product and multi-product configurations. A key finding is that the fitted nominal elasticities are positive. As a result, an unconstrained sales-maximizer would push every price to its upper bound, and the CPI ceiling is the safeguard that prevents this. Simulated Annealing instead settles on conservative, interior prices that lower consumer cost while still meeting the sales target. We benchmark forecast accuracy against naive, seasonal-naive, ARIMA, and SARIMA baselines, and a CPI-deflated re-specification shows that the positive nominal elasticities are largely an inflation-driven artifact. The result is a transparent, fairness-aware pricing framework.

Evaluating decisions made under uncertainty is hard when labeled outcomes are scarce, costly, or confounded with luck. We treat subjective expected utility (SEU) maximization as a stated standard and define a graded measure -- SEU sensitivity -- of an agent's conformity to it. The vehicle is a softmax choice model with a sensitivity parameter $α$ on SEU-valued alternatives; the contribution is a sequence of identifiability results for $α$ and for belief and utility parameters $(β, δ)$, validated in Stan via prior predictive checks, parameter recovery, and simulation-based calibration (SBC), with finite-sample caveats intact. In the uncertain-choice-only model $m_0$, $α$ is identifiable given the expected-utility vector $η$ and sharply recovered, while $(β, δ)$ are only weakly informed: the posterior barely contracts and concentrates on a $β$-$δ$ trade-off. In the extended model $m_1$, $δ$ becomes identifiable in principle via a $β$-free risky block, but its practical recovery gain at realistic sample sizes is negligible (matched-count CI-width reduction under 1%), and that block yields no detected $α$-precision gain at matched choice count. These are two distinct phenomena: for $δ$, identifiability does not imply precise estimability at realistic $n$; for $α$, identifiability is silent about what governs finite-$n$ precision. Marginal SBC passes for both models even where the joint posterior is weakly informed -- a demarcation we make precise. A two-by-two application (GPT-4o and Claude 3.5 Sonnet, each on insurance-claims triage and Ellsberg-style urns, with sampling temperature as the lever) runs end-to-end on real LLM choice data, detecting a structured comparative $α$ effect in two of four cells.

Environmental monitoring with unmanned aerial vehicles (UAVs) requires route planning methods that maximize covered area while handling energy limits, operational constraints, and geometric complexity. This paper reports the protocol and preliminary results of an ongoing systematic literature review (SLR) on autonomous UAV route planning for coverage-oriented environmental monitoring. The review follows the PRISMA 2020 framework and searches Scopus and Web of Science for studies published between 2015 and 2026. The protocol focuses on path planning, coverage path planning, and informative path planning, with emphasis on algorithmic families, coverage and energy metrics, obstacle handling, geometric environment representations, and environmental constraints. At the current stage, 562 records have been identified, 161 duplicates have been removed, and 401 unique records have been screened by title, abstract, and keywords. From these, 247 studies were retained for full-text eligibility assessment (235 eligible and 12 borderline records to be resolved during full-text review). A preliminary analysis of the retained studies suggests strong concentration on coverage-oriented formulations, multi-UAV coordination, and energy-aware optimization, while fewer studies explicitly address weather, uncertainty, or obstacle-rich environments. Most retained studies rely on simulation-based validation, highlighting a potential simulation-to-reality gap, and recent publications show increasing interest in reinforcement learning, hybrid optimization, and geometry-aware planning. These early findings indicate an active but fragmented research landscape and support the need for a structured synthesis to identify mature techniques and unresolved gaps for realistic environmental monitoring missions.

Episode mining aims to extract subsequences of events that possess certain distinctive properties and constitute facts valuable to the user. Maximal frequent episode mining concentrates on discovery of frequently-appearing subsequences, which are not included into any other larger frequent subsequence. The state-of-the-art for this problem is the MaxFEM algorithm which enumerates possible subsequences, while applying various pruning techniques to accelerate the search. However, this is a computationally-intensive problem: reducing the minimum number of required subsequence occurrences or increasing the length of the subsequence both substantially raise running time, which limits practical use of MaxFEM. In this paper we describe our efforts in designing a high-performing algorithm for this problem. For this we: 1) develop an efficient C++ implementation of MaxFEM, and 2) devise an efficient technique to parallelizing it. As the result, we propose an improved parallel MaxFEM variant, which we call ParMaxFEM. Additionally, we integrate the improved algorithm into Desbordante - a high-performance, open-source data profiler with deep Python integration that treats patterns as first-class entities and allows users to develop their custom programs that can include discovery and validation of patterns. To evaluate our approach we compare both C++ implementations with the original SPMF implementation. Experiments demonstrated that our reimplemented version provides up to $8\times$ speedup over the SPMF baseline, while our parallelization technique provides up to $35\times$ improvement overall (on 8 cores).

Sparse tangent portfolio optimization aims to learn an interpretable, low-cardinality portfolio in the tangency direction of the mean-variance frontier. However, the associated cardinality-constrained formulation is NP-hard, and standard predict-then-optimize pipelines often misalign forecasting accuracy with downstream portfolio quality. We propose an end-to-end decision-focused learning framework that reformulates Sharpe ratio maximization as a Disciplined Parametrized Programming (DPP)-compliant convex programming layer and replaces discrete selection with a smooth top-$k$ operator enforcing an exact cardinality $k$. This enables gradient flow through prediction, asset selection, and re-optimization, allowing the predictive model to directly optimize portfolio performance. Across four major equity markets, our method achieves competitive and often superior out-of-sample Sharpe ratios compared with historical and prediction-focused baselines, with particularly strong gains in larger asset universes. Our \href{https://github.com/feuerwerksh/Diffble-card-SR}{code} is publicly available.

I discuss conditions under which maximizing a proxy utility function is harmful and suggest this poses problems for applying decision theory.

Sparse rewards pose a central challenge in reinforcement learning, since agents receive no informative signal until they reach their goal. Intrinsic-reward methods address this issue by optimizing non-stationary objectives such as novelty, prediction error, or skill diversity, thereby injecting a supervision signal into the problem. While effective, these methods often require that the extrinsic (sparse) reward can be evaluated -- either online or during offline relabeling of the stored transitions. This limitation is particularly vexing for multi-task, meta-, and continual reinforcement learning, where agents' interactions with the environment are usually reward-free. In this work, we present a method to pre-train transferable exploration policies that rapidly adapt to sparse rewards at downstream task time. Our objective maximizes state-space covering for the occupancy measure, and can be framed in terms of entropy maximization. Its algorithmic implementation, ROVER, leverages recent advances on the operatorial formulation of RL to estimate occupancy with a learned resolvent world model, bypassing common hurdles associated with density and entropy estimation. ROVER further introduces a virtual "sink" state for unexplored regions, balancing coverage of known states with expansion into unseen ones and preventing cyclic expansion-collapse behavior during learning. In tabular and pixel-based sparse navigation tasks, ROVER produces more uniform aggregate coverage and stronger initializations for downstream tasks than standard reward-free baselines.

Next-generation wireless networks, including satellite-to-Open RAN systems, demand agile and intelligent resource management capable of handling dynamic multi-user interference under stochastic quality of service constraints. This paper introduces DIFFRACT, a neuralized utility maximization framework that leverages differentiable programming to integrate deep learning with optimization in wireless networks. Central to our approach is the exploitation of the mathematical structure of standard interference functions, which are foundational in wireless power control. By developing a duality theory for these functions, we map iterative interference management algorithms into differentiable neural network architectures via algorithm unrolling. This enables distributed, end-to-end gradient-based learning at the network edge, supporting real-time adaptation to interference in both terrestrial and non-terrestrial environments. DIFFRACT allows for scalable and robust utility maximization by modeling complex channel dynamics and leveraging the expressiveness of differentiable models. Experimental results confirm the framework's theoretical soundness and practical effectiveness for next-generation wireless systems.

Recently, the runtime analysis of multi-valued estimation-of-distribution algorithms in the framework of Ben Jedidia et al. (TCS 2024) has made significant advancements. However, almost all existing analyses are limited to multi-valued objective functions that in each dimension only distinguish between two types, also called categories, of values and hence can be treated with similar methods as pseudo-Boolean problems. Only recently, Adak and Witt (GECCO 2025) have presented a first runtime analysis of a multi-valued compact genetic algorithm (cGA) on the multi-valued OneMax function G-OneMax$\colon \{0,\dots,r-1\}^n \to \mathbf{N}$ defined by G-OneMax$(x_1,\dots,x_n)=\sum_{i=1}^n {x}_i$ and truly depending on all $r$ categories. We improve their runtime result from $\textrm{O}\bigl(n r^3 \log^2( n)\log (r)\bigr)$ to $\textrm{O}\bigl(n r \log^3(n)\log^3(r)\bigr)$, both for an optimal choice of the update strength $K$. Our result matches, up to polylogarithmic factors, the existing bound for the simpler $r$-valued OneMax function depending essentially only on two values and analyzed in several previous works. To show the new bound, we use improved drift theorems for processes with high self-loop probabilities and specifically derived concentration inequalities to analyze how probability mass in the multi-valued cGA moves into successively smaller and smaller intervals of the $r$-valued frequency matrix.

Many real-world classification tasks require predicting multiple labels per instance, necessitating the optimization of complex evaluation metrics such as the $F$-measure and Jaccard index. While the Empirical Utility Maximization (EUM) framework is natural for these population-level metrics, existing theoretical results are largely limited to asymptotic Bayes-consistency. In this paper, we develop principled learning algorithms for optimizing a broad class of generalized metrics within the EUM framework, grounded in the stronger notion of $H$-consistency. Our key contribution is the design of novel surrogate loss functions for multi-label learning that admit provable $H$-consistency bounds, enabling optimization with non-asymptotic guarantees tailored to the hypothesis class and finite samples. Crucially, we prove these combinatorially formulated surrogates decompose exactly, operating in strictly $O(l)$ time without approximations. Building on this foundation, we introduce MMO (Multi-Label Metric Optimization), a new family of algorithms for optimizing generalized linear-fractional metrics. We validate our approach through extensive experiments, demonstrating robust scalability and superior performance over state-of-the-art continuous baselines on large-scale datasets (MS-COCO, Reuters-21578) in high-sparsity, deep learning regimes. Our results offer both theoretical rigor and practical effectiveness for general multi-label metric optimization.

Tabular foundation models achieve strong accuracy on choice prediction tasks, but their predictions often violate the economic logic those tasks require: raising a price sometimes increases predicted demand, and implied willingness-to-pay estimates are frequently negative or implausible. We propose a two-stage adapter that embeds foundation model predictions within a utility-maximization framework. In the first stage, we estimate a standard choice model whose parameters are constrained to obey economic theory. In the second stage, we freeze those parameters and train a correction term that incorporates the foundation model's predictions as additional information. The result is a model that inherits the foundation model's accuracy gains while guaranteeing monotonic price-demand relationships under policy perturbation and producing analytically computable trade-off measures. On two transportation datasets, the adapter recovers up to 13 percentage points of accuracy over a standard logit model while maintaining perfect economic consistency, something neither the raw foundation models nor conventional distillation achieve.

We study the max-margin solutions reached by mirror flow in deep neural networks with homogeneous activation functions. Extending classical results on gradient flow, we derive a novel balance equation for mirror flow from convex duality, enabling a characterization of the horizon function governing the induced margin. We further establish max-margin characterizations together with convergence rates and norm growth estimates. Finally, we support our theory through experiments on synthetic datasets and standard vision tasks. Concretely, we show that: (1) distinct non-homogeneous mirror maps can induce the same max-margin solution; (2) convergence can be extremely slow, including exponentially slow regimes; and (3) although all considered mirror maps exhibit feature learning, they can produce markedly different representations, ranging from sparse to dense neuron activations. Together, these results provide a unified perspective on sparse and dense feature learning in homogeneous neural networks, highlighting how mirror maps shape both optimization dynamics and the geometry of the learned classifiers.

Graph Partitioning is a critical problem in numerous scientific and engineering domains including social network analysis, VLSI design, and many more. Spectral methods are known to produce quality partitions while minimizing edge cuts for a wide range of problems. However, the computational cost associated with the calculation of the Fiedler vector, an eigenvector associated with the second smallest eigenvalue of the graph Laplacian, remains a significant bottleneck due to memory issues and computational costs. In this paper, we present an accelerated approach to spectral bisection partitioning by replacing the traditional eigenvalue calculation with a simple artificial neural network model to approximate the Fiedler vector. We demonstrate that our approach achieves partitioning quality comparable to spectral bisection while significantly reducing the computational overhead, making it more scalable and efficient for large-scale problems

Bilateral trade models the task of intermediating between two strategic agents, a seller and a buyer, who wish to trade a good. We study this problem from the perspective of a profit-maximizing broker within an online learning framework, where the agents' valuations are generated by a smooth adversary. We devise a learning algorithm that guarantees a $\tilde{O}(\sqrt{T})$ regret bound, which is tight in the time horizon $T$ up to poly-logarithmic factors. This matches the minimax rate for the stochastic i.i.d. case, and is also well separated from the adversarial setting, where sublinear-regret is unattainable. By extending the strong regret guarantees from the i.i.d. case to the smooth adversary, we significantly broaden the scope of settings where such fast rate is achievable, while closing an important gap in the regret landscape of this fundamental economic problem. To overcome the challenges posed by this adversary, we leverage a continuity property of smooth instances and combines this with a hierarchical net-construction of the broker's action space, which is analyzed via algorithmic chaining. We showcase the applicability of these techniques by deriving a similarly tight $\tilde{O}(\sqrt{T})$ regret bound for a related mechanism design model: the joint ads problem.

Attributing model behavior to training data is an evolving research field. A common benchmark is data removal, which involves eliminating data instances with either low or high values, then assessing a model's performance trained on the modified dataset. Many existing studies leverage Shapley-based data values for this task. In this paper, we demonstrate that these data values are not optimally suited for pruning low-value data when only a limited amount of data remains. To address this limitation, we introduce the Constraint-Data-Value-Maximization (CDVM) approach, which effectively utilizes data attributions for pruning in low-data scenarios. By casting pruning as a constrained optimization that both maximizes total influence and penalizes excessive per-test contributions, CDVM delivers robust performance when only a small fraction of the data is retained. On the OpenDataVal benchmark, CDVM shows strong performance and competitive runtime.

This paper presents a hardware architecture that implements the Contrast Maximization (CM) algorithm in Field-Programmable Gate Array (FPGA) resources for event-based vision systems. CM estimates motion parameters by maximizing the contrast of an Image of Warped Events (IWE) reconstructed from asynchronous event streams. Event-based vision sensors generate sparse data with high temporal resolution and low spatial redundancy, which makes them well suited for hardware processing. The deterministic, massively parallel structure of the FPGA is leveraged to design a deeply pipelined architecture capable of high-throughput, energy-efficient processing suitable for real-time embedded applications. This paper details the hardware modules responsible for event warping, contrast computation, and iterative optimization, discusses key implementation decisions, and presents the hardware-aware optimization method used in the design. Experimental results demonstrate a substantial speed and efficiency improvement over CPU- and GPU-based implementations, with motion parameter estimation executing over 200 times faster. To the best of our knowledge, this is the first hardware architecture enabling acceleration of CM algorithm computations. Its performance is evaluated in terms of processing speed, energy efficiency, and hardware resource utilization. The proposed design is validated using an event-based object tracking application. The results confirm that the architecture provides a solid foundation for real-time motion estimation in high-speed, low-power embedded systems.

Standard rational actor models often attribute cooperation failures in social dilemmas to insufficient incentives, overlooking the destabilizing effects of continuous utility maximization. To address this, we propose a framework of will" defined as a mechanism that persistently pursues goals while ignoring local cost-benefit fluctuations. We formalize the Willed Agents as potential minimizers, distinguishing them from cumulative utility maximization. Dynamical analysis of infinite population demonstrates that willed agents shrink the feasible state space, acting as boundary constraints that accelerate convergence in canonical social dilemmas. Through multi-agent simulations in a spatiotemporal Stag Hunt Game, we show that willed agents function as cooperation catalysts", enabling groups to surmount high-risk thresholds where purely utility maximization fails. We find that heterogeneous will strength promotes cooperation, and that agents who autonomously suspend rational re-evaluation can significantly outperform continuous optimizers. These findings suggest that successful cooperation relies on the cognitive capacity to strategically constrain calculation.

Reinforcement learning (RL) for exponential-utility optimization in discounted Markov decision processes (MDPs) lacks principled value-based algorithms. We address this gap in the fixed risk-aversion setting. Building on the Bellman-type equation for exponential utility studied in \cite{porteus1975optimality}, we derive two Q-value-style extensions and show that the associated operators are contractions in the $L_\infty$ and sup-log/Thompson metrics, respectively. We characterize their fixed points and prove that the induced greedy stationary policy is optimal for the exponential-utility objective among stationary policies. These structural results lead to two model-free algorithms: a two-timescale Q-learning--style algorithm, for which we establish almost-sure convergence and provide finite-time convergence rates via timescale separation, and a one-timescale algorithm governed by a sublinear power-law operator. Since the latter does not admit a global contraction in standard metrics, we prove its convergence using delicate arguments based on local Lipschitzness, monotonicity, homogeneity, and Dini derivatives, and provide a scalar finite-time analysis that highlights the challenges in obtaining convergence rates in the vector case. Our work provides a foundation for value-based RL under exponential-utility objectives.

Regulatory approval of products in high-stakes domains such as drug development requires statistical evidence of safety and efficacy through large-scale randomized controlled trials. However, the high financial cost of these trials may deter developers who lack absolute certainty in their product's efficacy, ultimately stifling the development of `moonshot' products that could offer high social utility. To address this inefficiency, in this paper, we introduce a statistical protocol for experimentation where the product developer (the agent) conducts a randomized controlled trial sequentially and the regulator (the principal) partially subsidizes its cost. By modeling the protocol using a belief Markov decision process, we show that the agent's optimal strategy can be found efficiently using dynamic programming. Further, we show that the social utility is a piecewise linear and convex function over the subsidy level the principal selects, and thus the socially optimal subsidy can also be found efficiently using divide-and-conquer. Simulation experiments using publicly available data on antibiotic development and approval demonstrate that our statistical protocol can be used to increase social utility by more than 35$$\% relative to standard, non-sequential protocols.

Curating fully annotated datasets for medical image segmentation is labour-intensive and expertise-demanding. To alleviate this problem, prior studies have explored scribble annotations for weakly supervised segmentation. Existing solutions mainly compute losses on annotated areas and generate pseudo labels by propagating annotations to adjacent regions. However, these methods often suffer from inaccurate and unrealistic segmentations due to insufficient supervision and incomplete shape information. In contrast, we first investigate the principle of good scribble annotations, which leads to efficient scribble forms via supervision maximization and randomness simulation. We further introduce regularization terms to encode the spatial relationship and the shape constraints, where the EM algorithm is utilized to estimate the mixture ratios of label classes. These ratios are critical in identifying the unlabeled pixels for each class and correcting erroneous predictions, thus the accurate estimation lays the foundation for the incorporation of spatial prior. Finally, we integrate the efficient scribble supervision with the prior into a framework, referred to as ZScribbleSeg, and apply it to multiple scenarios. Leveraging only scribble annotations, ZScribbleSeg achieves competitive performance on six segmentation tasks including ACDC, MSCMRseg, BTCV, MyoPS, Decathlon-BrainTumor and Decathlon-Prostate. Our code will be released via https://github.com/DLwbm123/ZScribbleSeg.

Unsupervised pretraining has driven empirical advances in goal-conditioned reinforcement learning (GCRL), but its theoretical foundations remain poorly understood. In particular, an influential class of methods, mutual information skill learning (MISL), discovers behaviorally diverse skills that can later be used for downstream goal-reaching. However, it remains a theoretical mystery why skills learned through MISL should support goal-reaching. A subtle challenge is that both GCRL and MISL are umbrella terms: different GCRL tasks use distinct criteria for measuring goal-reaching performance, while different MISL methods optimize distinct notions of behavioral diversity. We address this challenge and unify GCRL and MISL as instances of control maximization. We identify three canonical GCRL formulations and prove that they are fundamentally inequivalent: they can induce incompatible optimal policies even in the same environment. Nevertheless, they all share a common interpretation: a well-performing goal-conditioned policy is one whose future trajectory is highly sensitive to the commanded goal, with the precise notion of sensitivity determined by the GCRL formulation. Noting that MISL objectives can be understood as measures of skill-sensitivity akin to goal-sensitivity, we show that MISL objectives are bounded by formulation-specific downstream goal-sensitivities. These bounds establish a precise correspondence between MISL methods and downstream GCRL tasks: for every GCRL formulation, there exists a matching MISL objective for which more diverse skills afford greater downstream goal sensitivity. Our results thus lay a theoretical foundation for RL pretraining and have important practical implications, such as suggesting which pretraining objectives to use when a user cares about a specific class of downstream tasks.

Artificial intelligence-generated content (AIGC) has emerged as a transformative paradigm for automating the creation of diverse and customized content, giving rise to rapidly growing computational workloads in cloud data centers. It is imperative for AIGC service providers (ASPs) to strategically schedule AIGC workloads to reduce data center energy costs while guaranteeing high-quality content generation. However, the distinctive characteristics of AIGC services pose critical challenges, including model heterogeneity across ASPs, implicit service quality evaluation, and complex inference process control. To tackle these challenges, we propose a joint energy management and coordinated AIGC workload scheduling framework, which introduces an explicit mathematical characterization of service quality to promote both job transfer among ASPs and fine-grained inference process configuration. Moreover, various energy resources within data centers are jointly considered to enhance power usage flexibility. Subsequently, a system utility maximization problem is formulated to balance AIGC service revenue with operational penalties and costs. Nevertheless, the strong coupling among job scheduling decisions induces severe reward sparsity, which limits the effectiveness of existing deep reinforcement learning (DRL) algorithms. To address this issue, we develop a diffusion model-aided reward shaping approach to synthesize complementary reward signals through a multi-step denoising process. This approach is seamlessly integrated with DRL to enable efficient learning of scheduling policies under sparse environmental feedback. Experiments based on real-world models and datasets demonstrate that our scheme effectively accommodates electricity price fluctuations and AIGC model heterogeneity, while achieving superior learning convergence and system utility compared with benchmark methods.

Learning curves are a fundamental primitive in supervised learning, describing how an algorithm's performance improves with more data and providing a quantitative measure of its generalization ability. Formally, a learning curve plots the decay of an algorithm's error for a fixed underlying distribution as a function of the number of training samples. Prior work on revenue-maximizing learning algorithms, starting with the seminal work of Cole and Roughgarden [STOC, 2014], adopts a distribution-free perspective, which parallels the PAC learning framework in learning theory. This approach evaluates performance against the hardest possible sequence of valuation distributions, one for each sample size, effectively defining the upper envelope of learning curves over all possible distributions, thus leading to error bounds that do not capture the shape of the learning curves. In this work we initiate the study of learning curves for revenue maximization and provide a near-complete characterization of their rate of decay in the basic setting of a single item and a single buyer. In the absence of any restriction on the valuation distribution, we show that there exists a Bayes-consistent algorithm, meaning that its learning curve converges to zero for any arbitrary valuation distribution as the number of samples $n \to \infty$. However, this convergence must be arbitrarily slow, even if the optimal revenue is finite. In contrast, if the optimal revenue is achieved by a finite price, then the optimal rate of decay is roughly $1/\sqrt{n}$. Finally, for distributions supported on discrete sets of values, we show that learning curves decay almost exponentially fast, a rate unattainable under the PAC framework.

We aim to learn a sparse and connected graph from sparse data, where the number of observations K can be substantially smaller than the signal dimension N for signals x in R^N, and the underlying distribution is unknown. In this severely ill-posed setting, we incorporate Fiedler number (the second eigenvalue of the graph Laplacian matrix that quantifies connectedness) as a robust regularization term in the sparse graph learning objective. We first develop a greedy algorithm that iteratively selects one edge globally for weakening/removal to reduce the objective, leveraging eigenvalue perturbation theorems that bound the adverse effect of an edge change to the Fiedler number. Next, we design a parallel variant, based on the Cheeger's inequality, that recursively partitions an input graph into two sub-graphs using an approximate Cheeger cut to distributedly find an optimal edge. Simulation experiments show that Fiedler number maximization robustifies sparse graph estimates, outperforming previous sparse graph learning algorithms.

Fractionally supervised classification (FSC) offers a flexible framework for combining labeled and unlabeled data in model-based classification, but existing formulations assume simple random sampling. In many applications, however, the retained observation is an extreme order statistic from a set rather than a randomly selected unit. This is particularly appealing when the target population is rare, since maxima nomination sampling (NS) can enrich the sample with the most informative observations, as in screening, environmental monitoring, repeated testing, and reliability studies. Under such designs, the likelihood function changes fundamentally, and the usual FSC EM construction is no longer valid. We develop FSC for nominated samples by introducing a latent representation that accounts for both the class membership of the observed maximum and the latent composition of the remaining units in the set. The resulting method yields a proper EM algorithm and a coherent weighted-likelihood FSC procedure for NS data. We present the methodology in general form, illustrate it for a rare-event contamination normal mixtures, and show through simulation that it substantially improves on the misspecified alternative by ignoring the extra rank information of such data. A real-data analysis demonstrates its practical value.

We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smooth (in some precise sense) with respect to some semi-metric, around one of its global maxima. Compared to previous works on bandits in general spaces (Kleinberg et al., 2008; Bubeck et al., 2011a) our algorithm does not require the knowledge of this semi-metric. Our algorithm, StoSOO, follows an optimistic strategy to iteratively construct upper confidence bounds over the hierarchical partitions of the function domain to decide which point to sample next. A finite-time analysis of StoSOO shows that it performs almost as well as the best specifically-tuned algorithms even though the local smoothness of the function is not known.

We introduce a new budgeted framework for online influence maximization, considering the total cost of an advertising campaign instead of the common cardinality constraint on a chosen influencer set. Our approach better models the real-world setting where the cost of influencers varies and advertisers want to find the best value for their overall social advertising budget. We propose an algorithm assuming an independent cascade diffusion model and edge level semi-bandit feedback, and provide both theoretical and experimental results. Our analysis is also valid for the cardinality constraint setting and improves the state of the art regret bound in this case.

We consider the design of smoothings of the (coordinate-wise) max function in $\mathbb{R}^d$ in the infinity norm. The LogSumExp function $f(x)=\ln(\sum^d_i\exp(x_i))$ provides a classical smoothing, differing from the max function in value by at most $\ln(d)$. We provide an elementary construction of a lower bound, establishing that every overestimating smoothing of the max function must differ by at least $\sim 0.8145\ln(d)$. Hence, LogSumExp is optimal up to small constant factors. However, we provide strictly stronger smoothings showing the entropy-based LogSumExp approach is not exactly optimal. In small dimensions, we propose exactly optimal smoothings, attaining our lower bound.

We propose FDRMFL, a task-driven multimodal feature extraction framework for federated regression under non-IID data distributions. Extracting predictive features from high-dimensional multimodal inputs is particularly challenging in this setting: data cannot leave each client, local samples are scarce and heterogeneously distributed, and unsupervised dimensionality reduction discards task-relevant information while federated training introduces representation drift across communication rounds. FDRMFL addresses these challenges through a unified four-term local objective: MSE prediction loss, a correlation-based mutual information surrogate that preserves dependence between the fused representation and the continuous target, a symmetric KL penalty that aligns cross-modal latent distributions before fusion, and an InfoNCE-style contrastive loss that anchors local representations to the global consensus. Experiments on three synthetic and two real-world near-infrared spectroscopy datasets under non-IID federated partitions, with comprehensive ablation and sensitivity analyses, demonstrate that each component contributes to the framework's effectiveness. FDRMFL reduces mean MSE by 33.8% relative to the best traditional baseline (PCA) and by 43.0% relative to VAE in simulation, and attains the lowest overall mean MSE among six federated algorithms including FedAvg, FedProx, MOON, SCAFFOLD, and FedBN.

Data unlearning aims to remove the influence of specific training samples from a trained model. In fine-tuning methods, data unlearning relies primarily on loss maximization over forget samples, which often leads to quality degradation or incomplete forgetting. Existing methods perform unlearning uniformly across diffusion stages, ignoring diffusion dynamics from noise to data. Our systematic study of diffusion phases shows that forgetting in diffusion models is uneven across time and frequency, with theoretical justification of distributive distortion and forgetting-utility trade-off. By selectively forgetting time and frequency in diffusion models, we achieve both higher unlearning success rates and improved generation quality across diverse settings, including both conditional and unconditional scenarios. We also introduce an improved SSCD metric that measures dissimilarity using a normalized perturbation distance. Together, we provide practical insights for understanding and improving data unlearning in diffusion models.

Generalized extreme value models capture dependence among choice alternatives in discrete choice modeling, but require this dependence to be predefined, symmetric, and shared uniformly across individuals. Recent efforts to synergize discrete choice models with deep neural networks have improved predictive performance but still cannot explicitly represent alternative dependence within neural architectures. To address these gaps, we introduce the alternative graph -- a graph in which nodes represent choice alternatives and edges encode their dependence -- and propose Alternative Graph Neural Networks (Alt-GNNs), a family of GNN-based discrete choice models that embed alternative dependence within a unified framework. Theoretically, Alt-GNNs incorporate multinomial logit, nested logit, and ASU-DNN as special cases and enable innovative model designs, including Nested Alt-GNN, Complete Alt-GNN, and Attention Alt-GNN. Alt-GNNs are consistent with random utility maximization theory, enforce behavioral constraints through alternative graphs, and offer a novel graph-based interpretation of utility functions. Empirically, on two travel mode choice datasets from London and Chicago, Alt-GNNs significantly improve predictive performance over all benchmark models in mode choice modeling because of their flexible alternative graph design and vast hyperparameter space. Even the simplest Alt-GNN variant -- Nested Alt-GNN -- generalizes the nested logit model while preserving its unique two-layer substitution properties, enabling graph-based behavioral constraints over otherwise unconstrained behavioral patterns from deep neural networks.

In this paper, we propose a Gaussian Process (GP)-based policy iteration framework for addressing both forward and inverse problems in Hamilton--Jacobi--Bellman (HJB) equations and mean field games (MFGs). Policy iteration is formulated as an alternating procedure between evaluating the value function under a fixed control policy and improving the policy. In our approach, we model the unknown fields using GPs within a policy-iteration framework that converts the nonlinear system into a sequence of linear PDE subproblems. Then, leveraging the linear structure, the updates for the value function and, in the MFG setting, the population density admit explicit representer formulas under linear PDE collocation constraints. The policy is subsequently updated pointwise via a Legendre transform step, which involves a low-dimensional maximization over the control variable. This maximization is explicit for standard quadratic costs. For smooth, strictly convex costs, this pointwise maximization is solved through its first-order optimality condition, whereas in constrained or non-smooth cases, it becomes a low-dimensional constrained maximization problem. To improve convergence, we incorporate the additive Schwarz acceleration as a preconditioning step following each policy update. Numerical experiments demonstrate the effectiveness of the Schwarz acceleration in improving computational efficiency.

Classical data valuation defines a data point's value through the finite marginal contribution $U(C\cup\{i\})-U(C)$, but estimating this quantity over coalitions requires repeated training and does not describe the contribution made along a stochastic training path. We ask whether marginal contributions of data points can be estimated from one coupled trajectory while retaining a verifiable relation to coalition-based values. To this end, we introduce Neural Dynamic Data Valuation (NDDV), which models each data point as a controlled stochastic state and computes a first-order marginal-contribution score via the adjoint equation of the Stochastic Maximum Principle (SMP). This raw sensitivity is then calibrated by a mass-preserving redistribution that increases one data point's participation while redistributing the same total weight over the remaining data points. We prove that the resulting backward adjoint recursion is the exact reverse-mode adjoint of the frozen-aggregate Euler system, bound its discrepancy from the mean-field sensitivity, and express each finite coalition marginal as an integral of local sample-weight sensitivities. These results yield pair-specific error bounds and sufficient conditions for ordering agreement with Shapley, Banzhaf, and leave-one-out values. Experiments on existing benchmarks evaluate marginal-contribution fidelity, score-release cost, corrupted-sample detection, ablations, and failure regimes. NDDV is a one-run, trajectory-conditioned estimator, not an unconditional replacement for cooperative-game values.

Many fairness criteria constrain the policy or choice of predictors, which can have unwanted consequences, in particular, when optimizing the policy under such constraints. Here, we in- stead suggest that fairness can be directly analyzed as a property of the utility function. Instead of imposing fairness constraints on the policy, we suggest to simply maximize a utility function satisfying certain fairness properties. Concretely, we define value of information fairness, which prescribes that there must not be an incentive to infer the protected attribute. This principle sug- gests modifying utility functions such that they satisfy value of information fairness. We describe how such modifications can be achieved and discuss consequences for the corresponding optimal policies. We apply our framework to thought experiments and the COMPAS data, demonstrating that focusing on utility functions sometimes provides answers that better align with intuitive judg- ments about what is fair. Moreover, we are not aware of any intuitively fair policy that violates value of information fairness; and when we find that value of information fairness recommends an intuitively unfair policy, no realizable policy is intuitively fair.