A Geometric Perspective on Optimal Representations for Reinforcement Learning
This work addresses representation learning for reinforcement learning practitioners, offering a theoretical framework that is incremental, building on existing concepts like proto-value functions.
The paper tackles the problem of representation learning in reinforcement learning by introducing a geometric perspective that optimizes representations to minimize approximation error for all stationary policies, showing that this reduces to predicting adversarial value functions (AVFs). The result demonstrates that using value functions as auxiliary tasks corresponds to an expected-error relaxation, with experiments on the four-room domain highlighting AVFs' usefulness.
We propose a new perspective on representation learning in reinforcement learning based on geometric properties of the space of value functions. We leverage this perspective to provide formal evidence regarding the usefulness of value functions as auxiliary tasks. Our formulation considers adapting the representation to minimize the (linear) approximation of the value function of all stationary policies for a given environment. We show that this optimization reduces to making accurate predictions regarding a special class of value functions which we call adversarial value functions (AVFs). We demonstrate that using value functions as auxiliary tasks corresponds to an expected-error relaxation of our formulation, with AVFs a natural candidate, and identify a close relationship with proto-value functions (Mahadevan, 2005). We highlight characteristics of AVFs and their usefulness as auxiliary tasks in a series of experiments on the four-room domain.