Shishen Lin

Per Kristian Lehre, Shishen Lin

Runtime analysis, as a branch of the theory of AI, studies how the number of iterations algorithms take before finding a solution (its runtime) depends on the design of the algorithm and the problem structure. Drift analysis is a state-of-the-art tool for estimating the runtime of randomised algorithms, such as evolutionary and bandit algorithms. Drift refers roughly to the expected progress towards the optimum per iteration. This paper considers the problem of deriving concentration tail-bounds on the runtime/regret of algorithms. It provides a novel drift theorem that gives precise exponential tail-bounds given positive, weak, zero and even negative drift. Previously, such exponential tail bounds were missing in the case of weak, zero, or negative drift. Our drift theorem can be used to prove a strong concentration of the runtime/regret of algorithms in AI. For example, we prove that the regret of the \rwab bandit algorithm is highly concentrated, while previous analyses only considered the expected regret. This means that the algorithm obtains the optimum within a given time frame with high probability, i.e. a form of algorithm reliability. Moreover, our theorem implies that the time needed by the co-evolutionary algorithm RLS-PD to obtain a Nash equilibrium in a \bilinear max-min-benchmark problem is highly concentrated. However, we also prove that the algorithm forgets the Nash equilibrium, and the time until this occurs is highly concentrated. This highlights a weakness in the RLS-PD which should be addressed by future work.

Shishen Lin

Learning in games is a fundamental problem in machine learning and artificial intelligence, with numerous applications~\citep{silver2016mastering,schrittwieser2020mastering}. This work investigates two-player zero-sum matrix games with an unknown payoff matrix and bandit feedback, where each player observes their actions and the corresponding noisy payoff. Prior studies have proposed algorithms for this setting~\citep{o2021matrix,maiti2023query,cai2024uncoupled}, with \citet{o2021matrix} demonstrating the effectiveness of deterministic optimism (e.g., \ucb) in achieving sublinear regret. However, the potential of randomised optimism in matrix games remains theoretically unexplored. We propose Competitive Co-evolutionary Bandit Learning (\coebl), a novel algorithm that integrates evolutionary algorithms (EAs) into the bandit framework to implement randomised optimism through EA variation operators. We prove that \coebl achieves sublinear regret, matching the performance of deterministic optimism-based methods. To the best of our knowledge, this is the first theoretical regret analysis of an evolutionary bandit learning algorithm in matrix games. Empirical evaluations on diverse matrix game benchmarks demonstrate that \coebl not only achieves sublinear regret but also consistently outperforms classical bandit algorithms, including \exptr~\citep{auer2002nonstochastic}, the variant \exptrni~\citep{cai2024uncoupled}, and \ucb~\citep{o2021matrix}. These results highlight the potential of evolutionary bandit learning, particularly the efficacy of randomised optimism via evolutionary algorithms in game-theoretic settings.