Online Action Learning in High Dimensions: A Conservative Perspective
This work addresses the need for safe and efficient online action learning in applications like dynamic pricing and auctions, offering a tunable conservative approach for practitioners.
The paper tackles the problem of sequential learning in high-dimensional contexts by extending the ε-greedy heuristic with a conservative directive, focusing search on promising actions to balance exploration and safety, and provides theoretical regret bounds and empirical validation.
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 $ε_t$-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 $ε_t$-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.