In this note, we investigate the robustness of Nash equilibria (NE) in multi-player aggregative games with coupling constraints. There are many algorithms for computing an NE of an aggregative game given a known aggregator. When the coupling parameters are affected by uncertainty, robust NE need to be computed. We consider a scenario where players' weight in the aggregator is unknown, making the aggregator kind of "a black box". We pursue a suitable learning approach to estimate the unknown aggregator by proposing an inverse variational inequality-based relationship. We then utilize the counterpart to reconstruct the game and obtain first-order conditions for robust NE in the worst case. Furthermore, we characterize the generalization property of the learning methodology via an upper bound on the violation probability. Simulation experiments show the effectiveness of the proposed inverse learning approach.

Decentralized finance exposes supervisors to fast-moving, networked credit risks. General-purpose LLM agents fit this setting poorly: they over-read weak evidence and recommend high-stakes interventions, while existing evaluations offer no regulator-aligned way to measure the resulting false alarms. We introduce DeXposure-Claw, a forecast-grounded agentic supervision system that routes LLM decisions through structured evidence: (1) DeXposure-FM, a graph time-series foundation model, forecasts future exposure networks; (2) deterministic monitors and stress scenarios then turn those forecasts into typed alerts, attribution signals, and scenario evidence; and (3) data-health and confidence gates constrain escalation before DeXposure-Claw emits auditable supervisory tickets with rationales. We further develop DeXposure-Bench, a six-axis evaluation harness, whose decision axis scores tickets against a regulator-aligned absolute-loss ground truth and an explicit false-intervention rate. Experiments on five years of weekly real data fully support our system. Code is at https://github.com/EVIEHub/DeXposure-Claw.

Multi-agent debate improves the reliability of large language models (LLMs) through iterative peer critiques. However, fixed topologies often introduce persistent positional biases, amplify unreliable agents, and cause high sensitivity to role assignments. We introduce Permutation-Equivariant Adaptive Routing Multi-Agent Debate (PEAR), an inference-time protocol that dynamically reconfigures communication roles and sparse topologies across consecutive debate rounds. By strategically switching agent-to-role assignments based on evolving agent states, PEAR prevents any agent from permanently occupying a privileged network position or distributes influence more evenly across the debate. We theoretically characterize PEAR as an equivariant sparse router: it preserves accuracy under agent relabeling while reducing routing complexity and improving generalization. Comprehensive empirical evaluations across four reasoning benchmarks and six diverse LLM backbones demonstrate PEAR significantly improves average accuracy over the strongest debate baselines. The code is at https://github.com/EVIEHub/PEAR.

In this paper, we study zero-sum potential team games with a supervisor network, where agents rely on supervisor-provided belief information rather than accurate common beliefs. The main challenge is that such belief information can be inaccurate because of supervisors' belief-estimation errors and the misreporting of joint actions by Byzantine teams. We propose the distributed team-orchestrating algorithm (DTOA), which combines team fictitious play with supervisor-based distributed belief learning. We prove the convergence of supervisors' belief estimates and establish that the induced learning dynamics converge to a near team-Nash equilibrium (TNE) in terms of the team-Nash gap (TNG). In the Byzantine setting, we consider a misreporting attack model and develop a Byzantine-resilient DTOA. We further provide probabilistic guarantees for Byzantine-team identification and establish an asymptotic bound on the honest TNG. Numerical experiments illustrate the theoretical findings, compare DTOA with baseline learning methods, and evaluate its performance in a Markov decision process setting.

We study safe online reinforcement learning in Constrained Markov Decision Processes (CMDPs) under strong regret and violation metrics, which forbid error cancellation over time. Existing primal-dual methods that achieve sublinear strong reward regret inevitably incur growing strong constraint violation or are restricted to average-iterate convergence due to inherent oscillations. To address these limitations, we propose the Flexible safety Domain Optimization via Margin-regularized Exploration (FlexDOME) algorithm, the first to provably achieve near-constant Õ(1) strong constraint violation alongside sublinear strong regret and non-asymptotic last-iterate convergence. FlexDOME incorporates time-varying safety margins and regularization terms into the primal-dual framework. Our theoretical analysis relies on a novel term-wise asymptotic dominance strategy, where the safety margin is rigorously scheduled to asymptotically majorize the functional decay rates of the optimization and statistical errors, thereby clamping cumulative violations to a near-constant level. Furthermore, we establish non-asymptotic last-iterate convergence guarantees via a policy-dual Lyapunov argument. Experiments corroborate our theoretical findings.

Neural operators approximate PDE solution maps, but they need not respect the symmetries of the governing equation. In out-of-distribution (OOD) regimes, a standard neural operator must often learn coordinate alignment and physical evolution within a single map, which can hurt generalization. We use known continuous symmetries of evolution equations on periodic domains to separate these two roles. We propose the Physics-Aligned Canonical Equivariant Fourier Neural Operator (PACE-FNO), which estimates the input frame with a Lie-algebra coordinate estimator, maps the field to a reference frame, applies a standard Fourier Neural Operator (FNO), and restores the prediction to the target frame. We train alignment and operator prediction jointly using bounded symmetry perturbations, with an optional low-dimensional refinement step that updates the estimated frame at inference. Equivariance is enforced by the input and output transformations, while the FNO architecture remains unchanged. Across 1-D and 2-D Burgers, shallow-water, and Navier-Stokes equations on periodic domains, PACE-FNO matches the in-distribution (ID) accuracy of standard neural operators and reduces out-of-distribution (OOD) relative error by up to 12x over FNO with symmetry augmentation (FNO+Aug) under translations and Galilean shifts, with smaller gains for coupled rotation-translation shifts. Ablations show that aligning the input and restoring the output frame account for most OOD gains; inference-time refinement provides a smaller correction.

Significant progress has been made in aligning LLMs with target value functions. We argue that, even when an LLM has been well aligned in (post-)training, it may still fail to maximise the aligned value in reasoning. We mathematically formalise this gap as rational value risk: the utility discrepancy between a model's deployed reasoning strategy and its rational counterpart, which is defined to be the responses that maximise expected utility in the steepest direction. The estimation error of rational value risk is further decomposed into three components from finite candidates, finite prompts, and imperfect verifiers. Extensive experiments are conducted, covering models Llama-3.1, Qwen-2.5, Tulu-3 families (7B-72B), GPT-5.2, GPT-5.5, and DeepSeek-V4, and benchmarks UltraFeedback, AlpacaEval, GSM8K, MATH, HumanEval, and MathArena. The results validate that (1) rational value risk is widespread; (2) value alignment can reduce, but cannot eliminate, it; (3) the risk is highly sensitive to inference-time reasoning strategy; and (4) longer reasoning improves rationality with diminishing returns. The code is at https://github.com/EVIEHub/LLM-Rationality.

Vision-language models (VLMs) can estimate physical quantities such as duration, speed, and acceleration from visual observations, but existing benchmarks primarily assess overall model performance against annotated ground truth. In deployment, a key question is whether an individual prediction can be trusted when its ground truth is unavailable. Self-consistency alone may fail to capture important failure modes: a VLM may produce stable-but-wrong estimates or rely on textual priors rather than visual evidence. We formulate answer-level selective prediction for quantitative physical reasoning and propose Answer-Level Trust Selection (ATS), a post-hoc, model-agnostic framework for accepting or rejecting individual VLM predictions. ATS requires no fine-tuning, auxiliary verifier, or access to the model's internal logits. Instead, it aggregates eight interpretable behavioral diagnostic scores derived from repeated queries and controlled interventions into a unified trust score. We evaluate ATS in depth on Qwen2.5-VL-7B and across 20 VLM backbones, examining selective performance, diagnostic behavior, and targeted failure modes. Our results show that intervention-based diagnostics help identify stable-but-wrong and prior-tracking predictions that repeated agreement alone may miss. However, improved failure-case rejection can come at the cost of lower retention of correct predictions. ATS therefore complements model-level capability evaluation with answer-level reliability assessment for quantitative VLM predictions. Code will be released upon publication.

LLM agents are promising for alpha mining via combining financial priors, symbolic reasoning, executable factor generation, and feedback-driven refinement. Yet, they face a combinatorial search space, noisy non-stationary feedback, redundant discoveries, and overfitting risks from naively reusing past successes. To address these challenges, we propose AlphaMemo, a self-evolving alpha mining agent with Structured Search-Process Memory. Rather than memorizing only final factors or full trajectories, AlphaMemo records reusable evidence about which edit motifs work or fail under specific parent-factor contexts. It extracts motifs from Abstract Syntax Tree (AST) differences, applies confidence-gated residual memory on top of a search-ledger prior, and uses asymmetric veto control to suppress high-confidence failure patterns. Experiments on CSI 500 and S&P 500 show improved out-of-sample performance and fixed-budget discovery efficiency, with ablations validating the roles of residual learning, confidence gating, AST-diff motifs, and veto memory. Code is at https://github.com/jarrettyu/AlphaMemo.

This work studies heterogeneous Multi-Objective Reinforcement Learning (MORL), where objectives can differ sharply in temporal frequency. Such heterogeneity allows dense objectives to dominate learning, while sparse long-horizon rewards receive weak credit assignment, leading to poor sample efficiency. We propose a Parallel Reward Integration with Symmetry (PRISM) algorithm that enforces reflectional symmetry as an inductive bias in aligning reward channels. PRISM introduces ReSymNet, a theory-motivated model that reconciles temporal-frequency mismatches across objectives, using residual blocks to learn a scaled opportunity value that accelerates exploration while preserving the optimal policy. We also propose SymReg, a reflectional equivariance regulariser that enforces agent mirroring and constrains policy search to a reflection-equivariant subspace. This restriction provably reduces hypothesis complexity and improves generalisation. Across MuJoCo benchmarks, PRISM consistently outperforms both a sparse-reward baseline and an oracle trained with full dense rewards, improving Pareto coverage and distributional balance: it achieves hypervolume gains exceeding 100\% over the baseline and up to 32\% over the oracle. The code is at \href{https://github.com/EVIEHub/PRISM}{https://github.com/EVIEHub/PRISM}.

Alignment and adaptation in large language models heavily rely on reinforcement learning from human feedback (RLHF); yet, theoretical understanding of its generalisability remains premature, especially when the learned reward could shift, and the KL control is estimated and clipped. To address this issue, we develop generalisation theory for RLHF that explicitly accounts for (1) reward shift: reward models are trained on preference data from earlier or mixed behaviour policies while RLHF optimises the current policy on its own rollouts; and (2) clipped KL regularisation: the KL regulariser is estimated from sampled log-probability ratios and then clipped for stabilisation, resulting in an error to RLHF. We present generalisation bounds for RLHF, suggesting that the generalisation error stems from a sampling error from prompts and rollouts, a reward shift error, and a KL clipping error. We also discuss special cases of (1) initialising RLHF parameters with a uniform prior over a finite space, and (2) training RLHF by stochastic gradient descent, as an Ornstein-Uhlenbeck process. The theory yields practical implications in (1) optimal KL clipping threshold, and (2) budget allocation in prompts, rollouts, and preference data.

Neurosymbolic systems such as DeepProbLog combine neural perception with probabilistic logic, but standard inference is associational. Counterfactual reasoning additionally requires a causal semantics for interventions and evidence. We introduce DeepSWIP, a single-world counterfactual semantics for DeepProbLog programs. Using neural materialization, we reduce fixed-context neural predicates to ordinary ProbLog choices, apply Single World Intervention Programs (SWIPs), and compute counterfactuals by weighted model counting (WMC) over a single transformed program. Under finite grounding and unique-supported-model assumptions, DeepSWIP is exact relative to the learned materialized FCM. The standard quotient-WMC form of ProbLog conditionals identifies active neural probabilities and explains intervention cleaning, calibration sensitivity, and rare-evidence instability. Experiments on MPI3D confirm the transformation against a DeepTwin construction against 12,000 queries, as predicted and a 2.14× inference speedup from avoiding the Twin's endogenous duplication. A SUMO HOV experiment shows that neural calibration degradation biases plug-in estimates, while a correctly scoped randomized-policy AIPW estimator removes most first-order bias for population mean and ATE estimands. Code is at https://github.com/saibib/deep_SWIP.

Global objectives, such as KL divergence and ELBO, are widely used in Bayesian inference for measuring distributional discrepancy. This paper studies their local-mass behaviour that is not directly captured by such objectives. We introduce and use two mathematical tools: (1) Mass Index for recording the polynomial and logarithmic decay scales of local mass, and (2) regularised extended KL (RE-KL), a set-localised divergence that can be formulated in the presence of singular components. Mass Indices help characterise how Bayesian updating changes local mass: (1) power-log likelihood factors shift it explicitly, and (2) parameter-dependent supports, or their smooth softenings, may change the local scale through the amount of mass that remains near the parameter value. Using local RE-KL, we prove absolute, relative, and directional inequalities for comparing local small-ball masses under the two KL directions. Together, these results provide a local theoretical account of local mass behaviour. Experiments provide controlled illustrations of the local behaviour. Code is available at https://github.com/Forsythia0604/Local-Mass-Framework.

Probabilistic Logic Programming (PLP) languages, like ProbLog, naturally support reasoning under uncertainty, while maintaining a declarative and interpretable framework. Meanwhile, counterfactual reasoning (i.e., answering “what if” questions) is critical for ensuring AI systems are robust and trustworthy; however, integrating this capability into PLP can be computationally prohibitive and unstable in accuracy. This paper addresses this challenge, by proposing an efficient program transformation for counterfactuals as Single World Intervention Programs (SWIPs) in ProbLog. By systematically splitting ProbLog clauses to observed and fixed components relevant to a counterfactual, we create a transformed program that (1) does not asymptotically exceed the computational complexity of existing methods, and is strictly smaller in common cases, and (2) reduces counterfactual reasoning to marginal inference over a simpler program. We formally prove the correctness of our approach, which relies on a weaker set independence assumptions and is consistent with conditional independencies, showing the resulting marginal probabilities match the counterfactual distributions of the underlying Structural Causal Model in wide domains. Our method achieves a 35% reduction in inference time versus existing methods in extensive experiments. This work makes complex counterfactual reasoning more computationally tractable and reliable, providing a crucial step towards developing more robust and explainable AI systems. The code is at https://github.com/EVIEHub/swip.

LLM-native advertising embeds sponsored content directly into model-generated responses, shifting the unit of sale from a fixed slot to a moment within an evolving conversation. Existing LLM ad-auction mechanisms primarily operate within a single response, settling the winner but not the timing. The extension is nontrivial: with one native insertion opportunity per session, the stopping time depends on bids, coupling timing with allocation, so static truthfulness arguments no longer apply. We propose the LLM-based Optimal Stopping Dynamic Auction (LLM-OSDA), a dynamic cost-per-click auction that integrates Bellman optimal stopping, winner allocation, and envelope pricing. A bid-independent LLM layer estimates contextual click quality and seamlessly renders the winning ad, while bids enter only the committed auction mechanism. Under an exact Bellman oracle, the expected discounted-click allocation is monotone in each advertiser's bid, and the corresponding envelope payment makes truthful bidding weakly dominant in expectation. For practical deployment, a learned StopNet approximates the Bellman action values. We show that its decisions differ from the optimal policy only near the stopping boundary and bound the resulting incentive loss in terms of its approximation error. Experiments on a simulated conversational advertising corpus show that LLM-OSDA improves net revenue by 11 percent over the strongest fixed-timing baseline while maintaining comparable user retention. Code is at https://github.com/2025Fang2025/llm-osda.

This paper proposes a suite of rationality measures and associated theory for reinforcement learning agents, a property increasingly critical yet rarely explored. We define an action in deployment to be perfectly rational if it maximises the hidden true value function in the steepest direction. The expected value discrepancy of a policy's actions against their rational counterparts, culminating over the trajectory in deployment, is defined to be expected rational risk; an empirical average version in training is also defined. Their difference, termed as rational risk gap, is decomposed into (1) an extrinsic component caused by environment shifts between training and deployment, and (2) an intrinsic one due to the algorithm's generalisability in a dynamic environment. They are upper bounded by, respectively, (1) the $1$-Wasserstein distance between transition kernels and initial state distributions in training and deployment, and (2) the empirical Rademacher complexity of the value function class. Our theory suggests hypotheses on the benefits from regularisers (including layer normalisation, $\ell_2$ regularisation, and weight normalisation) and domain randomisation, as well as the harm from environment shifts. Experiments are in full agreement with these hypotheses. The code is available at https://github.com/EVIEHub/Rationality.

Current bias evaluation methods rarely engage with communities impacted by AI systems. Inspired by bug bounties, bias bounties have been proposed as a reward-based method that involves communities in AI bias detection by asking users of AI systems to report biases they encounter when interacting with such systems. In the absence of a state-of-the-art review, this survey aimed to identify and analyse existing AI bias bounty programmes and to present academic literature on bias bounties. Google, Google Scholar, PhilPapers, and IEEE Xplore were searched, and five bias bounty programmes, as well as five research publications, were identified. All bias bounties were organised by U.S.-based organisations as time-limited contests, with public participation in four programmes and prize pools ranging from 7,000 to 24,000 USD. The five research publications included a report on the application of bug bounties to algorithmic harms, an article addressing Twitter's bias bounty, a proposal for bias bounties as an institutional mechanism to increase AI scrutiny, a workshop discussing bias bounties from queer perspectives, and an algorithmic framework for bias bounties. We argue that reducing the technical requirements to enter bounty programmes is important to include those without coding experience. Given the limited adoption of bias bounties, future efforts should explore the transferability of the best practices from bug bounties and examine how such programmes can be designed to be sensitive to underrepresented groups while lowering adoption barriers for organisations.

This paper studies constrained Markov decision processes (CMDPs) with constraints against stochastic thresholds, aiming at safety of reinforcement learning in unknown and uncertain environments. We leverage a Growing-Window estimator sampling from interactions with the uncertain environment to estimate the thresholds, based on which we design Stochastic Pessimistic-Optimistic Thresholding (SPOT), a novel model-based primal-dual algorithm for multiple constraints against stochastic thresholds. SPOT enables reinforcement learning under both pessimistic and optimistic threshold settings. We prove that our algorithm achieves sublinear regret and constraint violation; i.e., a reward regret of 𝒪̃(√(T)) while allowing an 𝒪̃(√(T)) constraint violation over T episodes. The theoretical guarantees show that our algorithm achieves performance comparable to that of an approach relying on fixed and clear thresholds. To the best of our knowledge, SPOT is the first reinforcement learning algorithm that realises theoretical guaranteed performance in an uncertain environment where even thresholds are unknown.

With the increasing penetration of machine learning applications in critical decision-making areas, calls for algorithmic fairness are more prominent. Although there have been various modalities to improve algorithmic fairness through learning with fairness constraints, their performance does not generalize well in the test set. A performance-promising fair algorithm with better generalizability is needed. This paper proposes a novel adaptive reweighing method to eliminate the impact of the distribution shifts between training and test data on model generalizability. Most previous reweighing methods propose to assign a unified weight for each (sub)group. Rather, our method granularly models the distance from the sample predictions to the decision boundary. Our adaptive reweighing method prioritizes samples closer to the decision boundary and assigns a higher weight to improve the generalizability of fair classifiers. Extensive experiments are performed to validate the generalizability of our adaptive priority reweighing method for accuracy and fairness measures (i.e., equal opportunity, equalized odds, and demographic parity) in tabular benchmarks. We also highlight the performance of our method in improving the fairness of language and vision models. The code is available at https://github.com/che2198/APW.

Prompt learning has attracted widespread attention in adapting vision-language models to downstream tasks. Existing methods largely rely on optimization strategies to ensure the task-awareness of learnable prompts. Due to the scarcity of task-specific data, overfitting is prone to occur. The resulting prompts often do not generalize well or exhibit limited task-awareness. To address this issue, we propose a novel Task-Aware Clustering (TAC) framework for prompting vision-language models, which increases the task-awareness of learnable prompts by introducing task-aware pre-context. The key ingredients are as follows: (a) generating task-aware pre-context based on task-aware clustering that can preserve the backbone structure of a downstream task with only a few clustering centers, (b) enhancing the task-awareness of learnable prompts by enabling them to interact with task-aware pre-context via the well-pretrained encoders, and (c) preventing the visual task-aware pre-context from interfering the interaction between patch embeddings by masked attention mechanism. Extensive experiments are conducted on benchmark datasets, covering the base-to-novel, domain generalization, and cross-dataset transfer settings. Ablation studies validate the effectiveness of key ingredients. Comparative results show the superiority of our TAC over competitive counterparts. The code is available at https://github.com/FushengHao/TAC.