Maximum Entropy
A Diffusion Model Framework for Maximum Entropy Reinforcement Learning
Sanokowski, Sebastian, Patil, Kaustubh, Knoll, Alois
Diffusion models have achieved remarkable success in data-driven learning and in sampling from complex, unnormalized target distributions. Building on this progress, we reinterpret Maximum Entropy Reinforcement Learning (MaxEntRL) as a diffusion model-based sampling problem. We tackle this problem by minimizing the reverse Kullback-Leibler (KL) divergence between the diffusion policy and the optimal policy distribution using a tractable upper bound. By applying the policy gradient theorem to this objective, we derive a modified surrogate objective for MaxEntRL that incorporates diffusion dynamics in a principled way. This leads to simple diffusion-based variants of Soft Actor-Critic (SAC), Proximal Policy Optimization (PPO) and Wasserstein Policy Optimization (WPO), termed DiffSAC, DiffPPO and DiffWPO. All of these methods require only minor implementation changes to their base algorithm. We find that on standard continuous control benchmarks, DiffSAC, DiffPPO and DiffWPO achieve better returns and higher sample efficiency than SAC and PPO.
Mind Your Entropy: From Maximum Entropy to Trajectory Entropy-Constrained RL
Zhan, Guojian, Wang, Likun, Wang, Pengcheng, Zhang, Feihong, Duan, Jingliang, Tomizuka, Masayoshi, Li, Shengbo Eben
Maximum entropy has become a mainstream off-policy reinforcement learning (RL) framework for balancing exploitation and exploration. However, two bottlenecks still limit further performance improvement: (1) non-stationary Q-value estimation caused by jointly injecting entropy and updating its weighting parameter, i.e., temperature; and (2) short-sighted local entropy tuning that adjusts temperature only according to the current single-step entropy, without considering the effect of cumulative entropy over time. In this paper, we extends maximum entropy framework by proposing a trajectory entropy-constrained reinforcement learning (TECRL) framework to address these two challenges. Within this framework, we first separately learn two Q-functions, one associated with reward and the other with entropy, ensuring clean and stable value targets unaffected by temperature updates. Then, the dedicated entropy Q-function, explicitly quantifying the expected cumulative entropy, enables us to enforce a trajectory entropy constraint and consequently control the policy long-term stochasticity. Building on this TECRL framework, we develop a practical off-policy algorithm, DSAC-E, by extending the state-of-the-art distributional soft actor-critic with three refinements (DSAC-T). Empirical results on the OpenAI Gym benchmark demonstrate that our DSAC-E can achieve higher returns and better stability.
Distributional Policy Evaluation: a Maximum Entropy approach to Representation Learning
In Distributional Reinforcement Learning (D-RL) [Bellemare et al., 2023], an agent aims to estimate Sutton and Barto, 2018], where the objective is to predict the expected return only. In Section 3, we answer this methodological question, showing that it is possible to reformulate Policy Evaluation in a distributional setting so that its performance index is explicitly intertwined with the representation of the (state or action) spaces.
Deriving the Scaled-Dot-Function via Maximum Likelihood Estimation and Maximum Entropy Approach
In this paper, we present a maximum likelihood estimation approach to determine the value vector in transformer models. We model the sequence of value vectors, key vectors, and the query vector as a sequence of Gaussian distributions. The variance in each Gaussian distribution depends on the time step, the corresponding key vector, and the query vector. The mean value in each Gaussian distribution depends on the time step, and the corresponding value vector. This analysis may offer a new explanation of the scaled-dot-product function or softmax function used in transformer architectures [1]. Another explanation, inspired by [4], is based on the maximum entropy approach in natural language processing [5]. In this approach, a query vector and key vectors are used to derive the feature functions for the maximum entropy model.