RL训练中，为什么熵减往往意味着训练收敛?

Core Insights - The article discusses the relationship between entropy reduction and convergence in reinforcement learning (RL) training, particularly focusing on softmax policies and their implications for strategy optimization [3][4]. Group 1: Entropy and Strategy Convergence - Entropy converging to zero indicates that the strategy is polarizing towards a deterministic solution, making it difficult to escape local optima, which is a key aspect of convergence [3][4]. - The first theoretical result indicates that for softmax strategies, the expected gradient norm of the strategy at state s is directly related to the Renyi-2 entropy, suggesting that as entropy approaches zero, the expected gradient norm also approaches zero [6][7]. - The second theoretical result shows that as entropy decreases, the upper bound on the movement of the strategy in terms of Reverse KL divergence also decreases, indicating a tighter convergence of strategies [8][16]. Group 2: Implications of Softmax Parameterization - The unique curvature properties of softmax parameterization lead to a decline in learning efficiency as entropy decreases, which can trap the model in local optima [17]. - The article suggests that alternative parameterizations, such as Newton's method or Hadamard parameterization, may help overcome the limitations imposed by softmax parameterization in RL training [17].