Deciding When to Switch: E-Processes for Adaptive Minimax Training for Generative Adversarial Nets

Modern data science increasingly gives rise to hypothesis-testing problems that are not naturally formulated in terms of parameters within prespecified statistical models. One important example is the dynamic evaluation of optimization algorithms, where decisions must be made during training about whether further updates remain beneficial or the algorithm should switch to a different phase. This issue is particularly relevant in stochastic min-max optimization. Generative adversarial networks (GANs) provide a canonical example, as their training requires repeated decisions about when to switch between discriminator and generator updates, yet existing methods typically rely on fixed update ratios or heuristic criteria. We formulate this switching problem as sequential hypothesis testing and develop an e-process-based adaptive training procedure. During discriminator updates, one e-process tests the null that the discriminator-induced separation between the empirical data distribution and the generator law remains below a target level. During generator updates, with the discriminator fixed, a second e-process tests the reverse null that this separation remains above a refresh level. Conditional on the observed training sample, we prove that fresh empirical indices and latent draws yield conditional e-values that can be accumulated into e-processes, providing anytime-valid Type I error control under adaptive model updates and data-dependent switching. Across multimodal synthetic distributions and image benchmark datasets, the proposed method matches or outperforms the best fixed-ratio baselines under several widely used GAN objectives.

Non-Asymptotic Best Policy Identification Guarantees in Online Reinforcement Learning

In this work we study the Best Policy Identification (BPI) problem in online, tabular Reinforcement Learning. This is an active sequential hypothesis testing problem in which the learner's objective is to identify an optimal policy in a Markov Decision Process (MDP) with high confidence, while minimizing the expected sample complexity to do so. We consider an online setting with deterministic rewards, where the agent must strategically navigate through the MDP in order to effectively explore. Previous works in the literature have provided asymptotically optimal methods for BPI, such as the Navigate and Stop (NaS) algorithm and its variants, however existing analysis remains asymptotic. In this work, we fill that gap by providing the first non-asymptotic sample complexity guarantees for NaS, showing that its sample complexity depends not only on the characteristic time, but also on the connectivity of the underlying MDP, the curvature of the optimal characteristic time, and other instance-dependent quantities. We identify these additional attributes and make explicit their contributions to the overall sample complexity.

Sequential Fairness Auditing with Limited Output Access

External evaluations are becoming increasingly central to the governance of AI systems. In practice, however, independent auditors often have limited access to deployed models and must rely on query-based interactions. Most existing fairness evaluation methods assume static datasets and fixed-sample statistical tests, making them poorly suited to real-world auditing scenarios in which evidence must be collected sequentially under query constraints. In this work, we formulate fairness auditing as a tolerance-aware sequential hypothesis-testing problem under limited model output access. We develop a sequential generalized likelihood-ratio framework that allows auditors to accumulate evidence from a finite audit pool and stop once sufficient support for compliance or violation has been obtained. The framework is instantiated for decision-based Statistical Parity and Equal Opportunity audits, and extended to score- and logit-based proxy audits when richer observables are available. Our results show that both the fairness metric and the level of model access significantly affect audit efficiency, and that the benefits of richer output information are not uniform across auditing settings. In particular, richer outputs can substantially reduce the number of queries required for some fairness metrics and operating regimes, while offering limited gains in near-threshold cases. This work provides a practical statistical framework for sequential fairness auditing under realistic deployment constraints.

Bayesian control for coding agents

Modern coding agents pair LLM generators with various tools, including cheap diagnostics and expensive verifiers. The tool-use decisions are typically governed by orchestrators that often use fixed rules and ignore uncertainty. We formulate orchestration as cost-sensitive sequential hypothesis testing: a Bayesian controller maintains a belief over candidate correctness and dynamically decides whether to gather more evidence, refine the candidate, verify it, or stop. Across six generators and nine coding benchmarks, Bayesian control proves to be most valuable when verification is costly and critics are informative but imperfect. Beyond control, the belief state yields an interpretable correctness score that outperforms token-probability and raw tool-success baselines for uncertainty quantification.

PACE: Anytime-Valid Acceptance Tests for Self-Evolving Agents

Self-evolving agents improve by repeatedly proposing changes to their own prompts, skills, or workflows and keeping those that score higher on a small held-out set. Almost all effort has gone into the proposer that generates candidates; we argue the weak point is the acceptor, the rule that decides whether to commit a change. Applied hundreds of times against the same noisy dev estimate, the ubiquitous "keep it if the score went up" rule is uncontrolled adaptive multiple testing: the agent effectively p-hacks itself, accumulating false commits that make it churn and drift rather than improve. We recast committing as a sequential hypothesis test and propose PACE (Paired Anytime-valid Commit Evaluation), a training-free, anytime-valid commit gate. Each candidate is compared to the incumbent on identical instances and committed only when a testing-by-betting e-process accumulates decisive evidence, stopping early to save evaluations and controlling each candidate's false-commit probability at a user-set level even under optional stopping (a per-decision guarantee). On Qwen2.5 agents (0.5B-3B) self-evolving at the prompt level on GSM8K, SVAMP, and ARC-Challenge, greedy acceptance commits 30-42% false and 10-33% harmful edits when a genuine improvement is hidden among noisy proposals, while PACE commits the real one and essentially nothing else, matching greedy's held-out accuracy at sharply lower variance and about 18% lower evaluation cost. With no real gain available, greedy commits 13-21 spurious self-modifications per run (72-100% false) and degrades the most fragile agent by 4.9 points, while PACE holds at baseline. Reliability of self-evolution depends on the acceptor, not only on the proposer.