Non-stationary Bandit Convex Optimization: A Comprehensive Study

• URL: http://arxiv.org/abs/2506.02980v1
• Date: Tue, 03 Jun 2025 15:18:41 GMT
• Title: Non-stationary Bandit Convex Optimization: A Comprehensive Study
• Authors: Xiaoqi Liu, Dorian Baudry, Julian Zimmert, Patrick Rebeschini, Arya Akhavan,
• Abstract summary: Bandit Convex Optimization is a class of sequential decision-making problems.<n>We study this problem in non-stationary environments.<n>We aim to minimize the regret under three standard measures of non-stationarity.
• Score: 28.086802754034828
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bandit Convex Optimization is a fundamental class of sequential decision-making problems, where the learner selects actions from a continuous domain and observes a loss (but not its gradient) at only one point per round. We study this problem in non-stationary environments, and aim to minimize the regret under three standard measures of non-stationarity: the number of switches $S$ in the comparator sequence, the total variation $\Delta$ of the loss functions, and the path-length $P$ of the comparator sequence. We propose a polynomial-time algorithm, Tilted Exponentially Weighted Average with Sleeping Experts (TEWA-SE), which adapts the sleeping experts framework from online convex optimization to the bandit setting. For strongly convex losses, we prove that TEWA-SE is minimax-optimal with respect to known $S$ and $\Delta$ by establishing matching upper and lower bounds. By equipping TEWA-SE with the Bandit-over-Bandit framework, we extend our analysis to environments with unknown non-stationarity measures. For general convex losses, we introduce a second algorithm, clipped Exploration by Optimization (cExO), based on exponential weights over a discretized action space. While not polynomial-time computable, this method achieves minimax-optimal regret with respect to known $S$ and $\Delta$, and improves on the best existing bounds with respect to $P$.

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