Principal-agent Bandit Games With Self-interested And Exploratory Learning Agents

Abstract

We study the repeated principal-agent bandit game, where the principal indirectly interacts with the unknown environment by proposing incentives for the agent to play arms. Most existing work assumes the agent has full knowledge of the reward means and always behaves greedily, but in many online marketplaces, the agent needs to learn the unknown environment and sometimes explore. Motivated by such settings, we model a self-interested learning agent with exploration behaviors who iteratively updates reward estimates and either selects an arm that maximizes the estimated reward plus incentive or explores arbitrarily with a certain probability. As a warm-up, we first consider a self-interested learning agent without exploration. We propose algorithms for both i.i.d. and linear reward settings with bandit feedback in a finite horizon \(T\), achieving regret bounds of \(\widetilde\{O\}(\sqrt\{T\})\) and \(\widetilde\{O\}( T^\{2/3\} )\), respectively. Specifically, these algorithms are estab

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