Challenging Common Assumptions in Convex Reinforcement Learning

TL;DR

This paper reveals that the common assumption equating finite and infinite trials objectives in convex RL is invalid, highlighting potential approximation errors and urging for revised methodologies in practical applications.

Contribution

It demonstrates that the equivalence between finite and infinite trials objectives in classic RL does not hold in convex RL, challenging a key assumption and proposing a need for new approaches.

Findings

Erroneous optimization of infinite trials objective causes significant approximation errors.

Finite trials setting differs from infinite trials in convex RL, impacting practical applications.

Shedding light on this issue can improve convex RL methodologies.

Abstract

The classic Reinforcement Learning (RL) formulation concerns the maximization of a scalar reward function. More recently, convex RL has been introduced to extend the RL formulation to all the objectives that are convex functions of the state distribution induced by a policy. Notably, convex RL covers several relevant applications that do not fall into the scalar formulation, including imitation learning, risk-averse RL, and pure exploration. In classic RL, it is common to optimize an infinite trials objective, which accounts for the state distribution instead of the empirical state visitation frequencies, even though the actual number of trajectories is always finite in practice. This is theoretically sound since the infinite trials and finite trials objectives can be proved to coincide and thus lead to the same optimal policy. In this paper, we show that this hidden assumption does not hold in the convex RL setting. In particular, we show that erroneously optimizing the infinite trials objective in place of the actual finite trials one, as it is usually done, can lead to a significant approximation error. Since the finite trials setting is the default in both simulated and real-world RL, we believe shedding light on this issue will lead to better approaches and methodologies for convex RL, impacting relevant research areas such as imitation learning, risk-averse RL, and pure exploration among others.