Online Action Learning in High Dimensions: A Conservative Perspective

TL;DR

This paper extends the $ ext{ extepsilon}_t$-greedy algorithm for high-dimensional sequential learning by incorporating a conservative approach that restricts exploration to promising actions, providing theoretical bounds and practical flexibility.

Contribution

It introduces a conservative high-dimensional $ ext{ extepsilon}_t$-greedy rule with theoretical regret bounds and practical tunability, improving upon non-conservative methods.

Findings

Bounded cumulative regret with high probability.

Lower bound on viable action set size improves regret bounds.

Flexible safety tuning without affecting theoretical guarantees.

Abstract

Sequential learning problems are common in several fields of research and practical applications. Examples include dynamic pricing and assortment, design of auctions and incentives and permeate a large number of sequential treatment experiments. In this paper, we extend one of the most popular learning solutions, the $\epsilon_t$-greedy heuristics, to high-dimensional contexts considering a conservative directive. We do this by allocating part of the time the original rule uses to adopt completely new actions to a more focused search in a restrictive set of promising actions. The resulting rule might be useful for practical applications that still values surprises, although at a decreasing rate, while also has restrictions on the adoption of unusual actions. With high probability, we find reasonable bounds for the cumulative regret of a conservative high-dimensional decaying $\epsilon_t$-greedy rule. Also, we provide a lower bound for the cardinality of the set of viable actions that implies in an improved regret bound for the conservative version when compared to its non-conservative counterpart. Additionally, we show that end-users have sufficient flexibility when establishing how much safety they want, since it can be tuned without impacting theoretical properties. We illustrate our proposal both in a simulation exercise and using a real dataset.