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Maximum Entropy Reinforcement Learning via Energy-Based Normalizing Flow

Chen-Hao Chao, Chien Feng, Wei-Fang Sun, Cheng-Kuang Lee, Simon See, Chun-Yi Lee

TL;DR

A new MaxEnt RL framework modeled using Energy-Based Normalizing Flows (EBFlow) that integrates the policy evaluation steps and the policy improvement steps, resulting in a single objective training process, and enables the calculation of the soft value function used in the policy evaluation target without Monte Carlo approximation.

Abstract

Existing Maximum-Entropy (MaxEnt) Reinforcement Learning (RL) methods for continuous action spaces are typically formulated based on actor-critic frameworks and optimized through alternating steps of policy evaluation and policy improvement. In the policy evaluation steps, the critic is updated to capture the soft Q-function. In the policy improvement steps, the actor is adjusted in accordance with the updated soft Q-function. In this paper, we introduce a new MaxEnt RL framework modeled using Energy-Based Normalizing Flows (EBFlow). This framework integrates the policy evaluation steps and the policy improvement steps, resulting in a single objective training process. Our method enables the calculation of the soft value function used in the policy evaluation target without Monte Carlo approximation. Moreover, this design supports the modeling of multi-modal action distributions while facilitating efficient action sampling. To evaluate the performance of our method, we conducted experiments on the MuJoCo benchmark suite and a number of high-dimensional robotic tasks simulated by Omniverse Isaac Gym. The evaluation results demonstrate that our method achieves superior performance compared to widely-adopted representative baselines.

Maximum Entropy Reinforcement Learning via Energy-Based Normalizing Flow

TL;DR

A new MaxEnt RL framework modeled using Energy-Based Normalizing Flows (EBFlow) that integrates the policy evaluation steps and the policy improvement steps, resulting in a single objective training process, and enables the calculation of the soft value function used in the policy evaluation target without Monte Carlo approximation.

Abstract

Existing Maximum-Entropy (MaxEnt) Reinforcement Learning (RL) methods for continuous action spaces are typically formulated based on actor-critic frameworks and optimized through alternating steps of policy evaluation and policy improvement. In the policy evaluation steps, the critic is updated to capture the soft Q-function. In the policy improvement steps, the actor is adjusted in accordance with the updated soft Q-function. In this paper, we introduce a new MaxEnt RL framework modeled using Energy-Based Normalizing Flows (EBFlow). This framework integrates the policy evaluation steps and the policy improvement steps, resulting in a single objective training process. Our method enables the calculation of the soft value function used in the policy evaluation target without Monte Carlo approximation. Moreover, this design supports the modeling of multi-modal action distributions while facilitating efficient action sampling. To evaluate the performance of our method, we conducted experiments on the MuJoCo benchmark suite and a number of high-dimensional robotic tasks simulated by Omniverse Isaac Gym. The evaluation results demonstrate that our method achieves superior performance compared to widely-adopted representative baselines.
Paper Structure (38 sections, 4 theorems, 22 equations, 13 figures, 4 tables)

This paper contains 38 sections, 4 theorems, 22 equations, 13 figures, 4 tables.

Key Result

Proposition 3.1

Eq. (eq:Q_value_function) satisfies the following statements: (1) Given that the Jacobian of $g_\theta$ is non-singular, $V_\theta ({\mathbf{s}}_t)\in \mathbb{R}$ and $Q_\theta({\mathbf{s}}_t, {\mathbf{a}}_t)\in \mathbb{R}$, $\forall {\mathbf{a}}_t \in{\mathcal{A}}, \forall {\mathbf{s}}_t \in {\math

Figures (13)

  • Figure 1: The Jacobian determinant products for (a) the non-linear and (b) the linear transformations, evaluated during training in the Hopper-v4 environment. Subfigure (b) is presented on a log scale for better visualization. This experiment adopt the affine coupling layers Dinh2016DensityEU as the nonlinear transformations.
  • Figure 2: (a) The soft value function and the trajectories generated using our method on the multi-goal environment. (b) The estimation error evaluated at the initial state under different choices of $M$.
  • Figure 3: The results in terms of total returns versus the number of training steps evaluated on five MuJoCo environments. Each curve represents the mean performance, with shaded areas indicating the 95% confidence intervals, derived from five independent runs with different seeds.
  • Figure 4: A comparison on six Isaac Gym environments. Each curve represents the mean performance of five runs, with shaded areas indicating the 95% confidence intervals. 'Steps' in the x-axis represents the number of training steps, each of which consists of $N$ parallelizable interactions with the environments.
  • Figure 5: A demonstration of the six Isaac Gym environments introduced in Section \ref{['sec:experiments:isaac']}. The dimensionalities of the state and action for each environment are denoted below each subfigure.
  • ...and 8 more figures

Theorems & Definitions (9)

  • Proposition 3.1
  • Proposition 3.2
  • Proposition A.1
  • proof
  • Remark A.2
  • proof
  • proof
  • Proposition A.3
  • proof