[演講公告] A Tutorial on Analyzing Machine Learning Algorithms
發布日期： 2025-09-16 公告單位： 數學系
主 講 人： 吳沛遠副教授 (臺灣大學電機工程學系)
演講題目：A Tutorial on Analyzing Machine Learning Algorithms
演講時間：2025年09月25日(星期四) 3:30 p.m.~ 5:00 p.m.
演講地點：中央大學鴻經館M107
Abstract：
This talk explores several foundational and emerging concepts at the intersection of machine learning theory, optimization, and reinforcement learning. We begin by presenting a novel perspective that frames self-taught reasoning in large language models (LLMs) through the lens of Markov chains, offering a probabilistic interpretation of multi-step in-context learning. We then investigate the convergence behavior of gradient descent under adversarial conditions, showing that with carefully controlled step sizes, gradient-based methods can still converge to the optimum even in the presence of perturbations, provided the objective satisfies smoothness and Polyak-Łojasiewicz (PL) conditions. Transitioning to sequential decision-making, we revisit the principle of Optimism in the Face of Uncertainty (OFU) and its implications for exploration strategies. We introduce a regret analysis of the Upper Confidence Bound (UCB) algorithm in the linear bandit setting, highlighting key theoretical guarantees. Finally, we examine the Least-Squares Value Iteration (LSVI) framework and its UCB-augmented variant (LSVI-UCB), which bridges supervised learning and reinforcement learning with provable exploration efficiency. Together, these topics emphasize the importance of structure, robustness, and principled exploration in modern learning systems.
演講題目：A Tutorial on Analyzing Machine Learning Algorithms
演講時間：2025年09月25日(星期四) 3:30 p.m.~ 5:00 p.m.
演講地點：中央大學鴻經館M107
Abstract：
This talk explores several foundational and emerging concepts at the intersection of machine learning theory, optimization, and reinforcement learning. We begin by presenting a novel perspective that frames self-taught reasoning in large language models (LLMs) through the lens of Markov chains, offering a probabilistic interpretation of multi-step in-context learning. We then investigate the convergence behavior of gradient descent under adversarial conditions, showing that with carefully controlled step sizes, gradient-based methods can still converge to the optimum even in the presence of perturbations, provided the objective satisfies smoothness and Polyak-Łojasiewicz (PL) conditions. Transitioning to sequential decision-making, we revisit the principle of Optimism in the Face of Uncertainty (OFU) and its implications for exploration strategies. We introduce a regret analysis of the Upper Confidence Bound (UCB) algorithm in the linear bandit setting, highlighting key theoretical guarantees. Finally, we examine the Least-Squares Value Iteration (LSVI) framework and its UCB-augmented variant (LSVI-UCB), which bridges supervised learning and reinforcement learning with provable exploration efficiency. Together, these topics emphasize the importance of structure, robustness, and principled exploration in modern learning systems.
更新日期: 2025-09-17
公告類別: 演講
瀏覽人次: 113