New Algorithms Offer Instance-Dependent Regret Bounds for Zero‑Sum Bandit Games

Global: New Algorithms Offer Instance-Dependent Regret Bounds for Zero‑Sum Bandit Games

Researchers have introduced three novel algorithms that apply the Explore‑Then‑Commit (ETC) framework to two‑player zero‑sum games with bandit feedback, as detailed in a preprint posted to arXiv in June 2025. The work aims to identify pure‑strategy Nash equilibria while providing instance‑dependent regret analyses, addressing a gap in the existing literature on adversarial game learning.

Algorithmic Framework

The proposed suite adapts the classic ETC approach to a competitive setting, incorporating mechanisms for both exploration and strategic commitment. By structuring the learning process into an initial exploration phase followed by a commitment to the empirically best action pair, the algorithms seek to balance information gathering with payoff maximization.

Baseline ETC Adaptation

The first algorithm extends ETC directly to zero‑sum games, offering a regret upper bound of O(Δ + √T) after T rounds, where Δ denotes the suboptimality gap between the optimal and second‑best action pairs. This result aligns the performance of ETC‑based methods with that of more specialized game‑learning techniques.

Adaptive Elimination Strategy

The second algorithm introduces an adaptive elimination procedure that leverages the ε‑Nash equilibrium property to prune suboptimal actions efficiently. Its regret bound scales as O(log(T Δ²)/Δ), reflecting a logarithmic dependence on the time horizon and a linear dependence on the inverse gap.

Non‑Uniform Exploration Variant

A third variant builds on the adaptive elimination method by employing non‑uniform exploration probabilities, further refining the selection of promising actions. This extension retains the same O(log(T Δ²)/Δ) regret guarantee while offering potential practical improvements in convergence speed.

Implications for Game Theory Research

Collectively, the findings demonstrate that ETC‑based algorithms can achieve competitive, instance‑dependent regret bounds in adversarial zero‑sum environments. The authors suggest that these results may inform future designs of learning agents in competitive domains, where bandit feedback limits direct observation of opponent payoffs.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.