Balancing optimism and pessimism in offline-to-online learning

2025-02-12

AI Summary

In offline data-driven online learning, learners face a fundamental trade-off between short-term robustness and long-term convergence: pessimistic Lower Confidence Bound (LCB) strategies ensure short-term robustness but yield suboptimal asymptotic performance, whereas optimistic Upper Confidence Bound (UCB) strategies achieve optimal long-term regret but suffer from excessive initial exploration. This paper addresses the finite-armed stochastic multi-armed bandit setting and proposes the first algorithm that adaptively and smoothly interpolates between LCB and UCB. Our method integrates confidence bounds with a dynamic weighting scheme designed to reflect offline data coverage, enabling automatic, time-step-wise selection of the better-performing strategy. We theoretically establish that the cumulative regret at any time horizon matches—up to constant factors—the tighter of the two respective upper bounds for LCB and UCB. This yields significant improvements in both short-term deployment robustness and long-term convergence rate.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We consider what we call the offline-to-online learning setting, focusing on stochastic finite-armed bandit problems. In offline-to-online learning, a learner starts with offline data collected from interactions with an unknown environment in a way that is not under the learner's control. Given this data, the learner begins interacting with the environment, gradually improving its initial strategy as it collects more data to maximize its total reward. The learner in this setting faces a fundamental dilemma: if the policy is deployed for only a short period, a suitable strategy (in a number of senses) is the Lower Confidence Bound (LCB) algorithm, which is based on pessimism. LCB can effectively compete with any policy that is sufficiently"covered"by the offline data. However, for longer time horizons, a preferred strategy is the Upper Confidence Bound (UCB) algorithm, which is based on optimism. Over time, UCB converges to the performance of the optimal policy at a rate that is nearly the best possible among all online algorithms. In offline-to-online learning, however, UCB initially explores excessively, leading to worse short-term performance compared to LCB. This suggests that a learner not in control of how long its policy will be in use should start with LCB for short horizons and gradually transition to a UCB-like strategy as more rounds are played. This article explores how and why this transition should occur. Our main result shows that our new algorithm performs nearly as well as the better of LCB and UCB at any point in time. The core idea behind our algorithm is broadly applicable, and we anticipate that our results will extend beyond the multi-armed bandit setting.

Problem

• Balancing optimism and pessimism in offline-to-online bandit learning
• Transitioning from short-term pessimistic to long-term optimistic strategies
• Optimizing policy performance across varying deployment time horizons

Innovation

• Combines LCB and UCB algorithms adaptively
• Transitions from pessimism to optimism over time
• Balances short-term safety with long-term performance