协同进化与赌博机学习算法的集中尾界分析
Concentration Tail-Bound Analysis of Coevolutionary and Bandit Learning Algorithms
AI总结：
该研究提出一种可适配多种漂移场景的新颖漂移定理，填补了弱/零/负漂移下指数尾界的空白，证明了两类智能算法性能的强集中性，同时发现了协同进化算法的纳什均衡遗忘弱点。
摘要：
运行时分析作为人工智能理论的一个分支，研究算法在找到解之前所需的迭代次数（即运行时）如何取决于算法设计和问题结构。漂移分析是估计进化算法、赌博机算法等随机算法运行时的前沿工具，漂移大致指每次迭代向最优解推进的期望进度。\n本文研究推导算法运行时/悔值的集中尾界问题，提出了一个新颖的漂移定理，可在正漂移、弱漂移、零漂移甚至负漂移情况下给出精确的指数尾界。此前，弱漂移、零漂移或负漂移场景下的这类指数尾界一直是缺失的。\n我们的漂移定理可用于证明人工智能算法运行时/悔值的强集中性。例如，我们证明了\rwab赌博机算法的悔值具有高度集中性，而此前的分析仅考虑了期望悔值。这意味着该算法能以高概率在给定时间框架内得到最优解，即一种算法可靠性形式。此外，我们的定理表明，协同进化算法RLS-PD在\bilinear最大-最小基准问题中获得纳什均衡所需的时间具有高度集中性。但我们也证明该算法会遗忘纳什均衡，且发生遗忘的时间也高度集中，这凸显了RLS-PD的一个弱点，有待未来研究解决。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
