Simple framework connects swapping actions to adapting over time
From Switching to Dynamic Regret: A Simple Reduction via Unbiased Random Sequences
Machine Learning
Summary
When learning from changing situations over time, it's hard to perform as well as a moving target. The paper shows how to translate the challenge of adapting to many changes into the easier problem of handling a few switches. The authors introduce a way to create a random sequence that mimics the changing target but only switches a few times with controlled randomness. This connection lets existing methods solve dynamic challenges more simply and with proven optimal performance.
What this means in practice
- •For machine learning engineers: Design online algorithms that adapt efficiently to changing environments with guaranteed optimal performance bounds.
- •For algorithm designers: Simplify analysis by converting dynamic regret problems into switching regret problems when optimizing iterative decision processes.
Authors
Yibo Wang, Wenhao Yang, Sifan Yang, Yuanyu Wan, Lijun Zhang
Abstract
In non-stationary online learning, dynamic regret has attracted increasing attention as a measure of how well an online learner performs against a time-varying comparator sequence. Despite considerable advances, attaining optimal bounds for strongly convex and exp-concave losses often involves intricate analysis. In this paper, we present a \textit{simple} framework that reduces dynamic regret minimization to switching regret minimization. As a result, we can derive dynamic regret bounds by using off-the-shelf algorithms with switching regret guarantees. The key idea of our reduction is to construct, for \textit{any} comparator sequence, an auxiliary random sequence that is unbiased at each round, with the controlled variance and a manageable number of switches. Combining this construction with suitable surrogate losses, we can decompose dynamic regret into the expected switching regret against the random sequence and its controlled variance. Theoretically, for strongly convex and exp-concave losses, we establish the $\widetilde{O}(T^{1/3}P_T^{2/3})$ dynamic regret bounds, where $T$ denotes the time horizon and $P_T$ denotes the path-length of the comparator sequence. Moreover, for general convex losses, the same reduction also recovers the $O(\sqrt{T(1+P_T)})$ dynamic regret bound. Notably, all our findings match the minimax optimal results for these three types of losses, highlighting the versatility of our proposed framework.