What about Inputting Policy in Value Function: Policy Representation and Policy-Extended Value Function Approximator

Abstract

We study Policy-extended Value Function Approximator (PeVFA) in Reinforcement Learning (RL), which extends conventional value function approximator (VFA) to take as input not only the state (and action) but also an explicit policy representation. Such an extension enables PeVFA to preserve values of multiple policies at the same time and brings an appealing characteristic, i.e., value generalization among policies. We formally analyze the value generalization under Generalized Policy Iteration (GPI). From theoretical and empirical lens, we show that generalized value estimates offered by PeVFA may have lower initial approximation error to true values of successive policies, which is expected to improve consecutive value approximation during GPI. Based on above clues, we introduce a new form of GPI with PeVFA which leverages the value generalization along policy improvement path. Moreover, we propose a representation learning framework for RL policy, providing several approaches to learn effective policy embeddings from policy network parameters or state-action pairs. In our experiments, we evaluate the efficacy of value generalization offered by PeVFA and policy representation learning in several OpenAI Gym continuous control tasks. For a representative instance of algorithm implementation, Proximal Policy Optimization (PPO) re-implemented under the paradigm of GPI with PeVFA achieves about 40% performance improvement on its vanilla counterpart in most environments.

ERL-Re$^2$: Efficient Evolutionary Reinforcement Learning with Shared State Representation and Individual Policy Representation

“…To our knowledge, PeVFA (Tang et al, 2020) and related variants are trained in an on-policy fashion in prior works. In the original paper of PeVFA, a newly implemented PPO algorithm, called PPO-PeVFA is studied.…”

“…Conventional value functions are defined on a specific policy. Recently, a new extension called Policy-extended Value Function Approximator (PeVFA) (Tang et al, 2020) is proposed to preserve the values of multiple policies. Concretely, given some representation χ π of policy π, a PeVFA parameterized by θ takes as input χ π additionally, i.e., Q θ (s, a, χ π ).…”

“…In our work, we adopt PeVFA for the value estimation of the EA population, which naturally fits the ability of PeVFA well. Additionally, different from the on-policy learning of PeVFA adopted in (Tang et al, 2020), we propose a new off-policy learning algorithm of PeVFA which is described later.…”