Tiered Reinforcement Learning: Pessimism in the Face of Uncertainty and Constant Regret

TL;DR

This paper introduces a tiered reinforcement learning framework that separates policies for risk-tolerant and risk-averse users, demonstrating that a specialized exploitation policy can achieve constant regret for risk-averse users, unlike standard online RL.

Contribution

The paper proposes a novel tiered RL approach with separate policies for different user risk profiles and shows that using Pessimistic Value Iteration yields constant regret for risk-averse users.

Findings

Separation of policies does not benefit minimax regret in the gap-independent setting.

Using Pessimistic Value Iteration achieves constant regret for risk-averse users.

Online regret remains optimal for risk-tolerant users despite the tiered approach.

Abstract

We propose a new learning framework that captures the tiered structure of many real-world user-interaction applications, where the users can be divided into two groups based on their different tolerance on exploration risks and should be treated separately. In this setting, we simultaneously maintain two policies $\pi^{\text{O}}$ and $\pi^{\text{E}}$: $\pi^{\text{O}}$ ("O" for "online") interacts with more risk-tolerant users from the first tier and minimizes regret by balancing exploration and exploitation as usual, while $\pi^{\text{E}}$ ("E" for "exploit") exclusively focuses on exploitation for risk-averse users from the second tier utilizing the data collected so far. An important question is whether such a separation yields advantages over the standard online setting (i.e., $\pi^{\text{E}}=\pi^{\text{O}}$) for the risk-averse users. We individually consider the gap-independent vs.~gap-dependent settings. For the former, we prove that the separation is indeed not beneficial from a minimax perspective. For the latter, we show that if choosing Pessimistic Value Iteration as the exploitation algorithm to produce $\pi^{\text{E}}$, we can achieve a constant regret for risk-averse users independent of the number of episodes $K$, which is in sharp contrast to the $\Omega(\log K)$ regret for any online RL algorithms in the same setting, while the regret of $\pi^{\text{O}}$ (almost) maintains its online regret optimality and does not need to compromise for the success of $\pi^{\text{E}}$.