[论文解读] Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning

Stefan Elfwing, Eiji Uchibe+1 more|arXiv (Cornell University)|Feb 10, 2017

Reinforcement Learning in Robotics参考文献 21被引用 72

一句话总结

引入用于强化学习神经网络的 SiLU 和 dSiLU 激活函数，并展示在使用就地 TD/Sarsa 的资格迹和 softmax 动作选择时，它们在 SZ-Tetris、10x10 Tetris 和 Atari 2600 上能够超越 DQN/DQN 变体。

ABSTRACT

In recent years, neural networks have enjoyed a renaissance as function approximators in reinforcement learning. Two decades after Tesauro's TD-Gammon achieved near top-level human performance in backgammon, the deep reinforcement learning algorithm DQN achieved human-level performance in many Atari 2600 games. The purpose of this study is twofold. First, we propose two activation functions for neural network function approximation in reinforcement learning: the sigmoid-weighted linear unit (SiLU) and its derivative function (dSiLU). The activation of the SiLU is computed by the sigmoid function multiplied by its input. Second, we suggest that the more traditional approach of using on-policy learning with eligibility traces, instead of experience replay, and softmax action selection with simple annealing can be competitive with DQN, without the need for a separate target network. We validate our proposed approach by, first, achieving new state-of-the-art results in both stochastic SZ-Tetris and Tetris with a small 10$ imes$10 board, using TD($λ$) learning and shallow dSiLU network agents, and, then, by outperforming DQN in the Atari 2600 domain by using a deep Sarsa($λ$) agent with SiLU and dSiLU hidden units.

研究动机与目标

• Motivate the use of sigmoid-weighted linear units (SiLU) and their derivative (dSiLU) as activation functions for neural network function approximators in reinforcement learning.
• Compare on-policy TD(lambda) and Sarsa(lambda) learning with eligibility traces against deep Q-learning variants.
• Demonstrate state-of-the-art performance on stochastic SZ-Tetris, 10x10 Tetris, and Atari 2600 using SiLU/dSiLU networks.
• Explore the impact of softmax action selection versus epsilon-greedy exploration in high-dimensional domains.

提出的方法

• Define SiLU activation a_k(s) = z_k * sigma(z_k) where z_k is the pre-activation of hidden unit k.
• Define dSiLU activation a_k(s) = sigma(z_k) * (1 + z_k*(1 - sigma(z_k))).
• Use TD(lambda) for V^pi and Sarsa(lambda) for Q^pi with gradient-descent updates theta_{t+1} = theta_t + alpha * delta_t * e_t and eligibility traces e_t.
• Compute gradients for SiLU and dSiLU via equations (11) and (12).
• Apply softmax action selection with Boltzmann distribution; anneal temperature tau over episodes.
• Evaluate on SZ-Tetris (shallow and deep nets), 10x10 Tetris, and Atari 2600 with SiLU/dSiLU networks.

实验结果

研究问题

• RQ1 How do SiLU and dSiLU activation functions affect learning performance in reinforcement learning compared to traditional activations (ReLU, sigmoid)?
• RQ2 Can on-policy TD(lambda)/Sarsa(lambda) with eligibility traces and softmax action selection compete with DQN/Double DQN on benchmark tasks?
• RQ3 Do deep architectures with SiLU/dSiLU outperform prior state-of-the-art on SZ-Tetris, 10x10 Tetris, and Atari 2600?
• RQ4 What is the impact of softmax versus epsilon-greedy exploration in these domains when using SiLU/dSiLU networks?

主要发现

• Shallow SiLU/dSiLU networks outperform ReLU and sigmoid on stochastic SZ-Tetris, with dSiLU achieving the best final average score (263) and best run (320).
• Deep SiLU-dSiLU networks outperform SiLU-SiLU and ReLU-ReLU on SZ-Tetris; mean final score 229, with higher performance than prior state-of-the-art.
• In 10x10 Tetris, a dSiLU network with 250 hidden units achieves a new state-of-the-art mean final score (4,900) and best run (5,300).
• Atari 2600 with a deep SiLU-dSiLU agent outperforms DQN/Double DQN in mean and median DQN-normalized scores across 12 games (mean 332%, median 125%).
• TD(lambda) and Sarsa(lambda) provide accurate value estimates without the max-overestimation bias seen in Q-learning-based methods.