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Register a new userQ-Learning with Differential Entropy of Q-Tables
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It is well-known that information loss can occur in the classic and simple Q-learning algorithm. Entropy-based policy search methods were introduced to replace Q-learning and to design algorithms that are more robust against information loss. We conjecture that the reduction in performance during prolonged training sessions of Q-learning is caused by a loss of information, which is non-transparent when only examining the cumulative reward without changing the Q-learning algorithm itself. We introduce Differential Entropy of Q-tables (DE-QT) as an external information loss detector to the Q-learning algorithm. The behaviour of DE-QT over training episodes is analyzed to find an appropriate stopping criterion during training. The results reveal that DE-QT can detect the most appropriate stopping point, where a balance between a high success rate and a high efficiency is met for classic Q-Learning algorithm.
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Entropy augmented to reward is known to soften the greedy argmax policy to softmax policy. Entropy augmentation is reformulated and leads to a motivation to introduce an additional entropy term to the objective function in the form of KL-divergence to regularize optimization process. It results in a policy which monotonically improves while interpolating from the current policy to the softmax greedy policy. This policy is used to build a continuously parameterized algorithm which optimize policy and Q-function simultaneously and whose extreme limits correspond to policy gradient and Q-learning, respectively. Experiments show that there can be a performance gain using an intermediate algorithm.
We investigate the evolution of the Q values for the implementation of Deep Q Learning (DQL) in the Stable Baselines library. Stable Baselines incorporates the latest Reinforcement Learning techniques and achieves superhuman performance in many game environments. However, for some simple non-game environments, the DQL in Stable Baselines can struggle to find the correct actions. In this paper we aim to understand the types of environment where this suboptimal behavior can happen, and also investigate the corresponding evolution of the Q values for individual states. We compare a smart TrafficLight environment (where performance is poor) with the AI Gym FrozenLake environment (where performance is perfect). We observe that DQL struggles with TrafficLight because actions are reversible and hence the Q values in a given state are closer than in FrozenLake. We then investigate the evolution of the Q values using a recent decomposition technique of Achiam et al.. We observe that for TrafficLight, the function approximation error and the complex relationships between the states lead to a situation where some Q values meander far from optimal.
In this paper, we establish a theoretical comparison between the asymptotic mean-squared error of Double Q-learning and Q-learning. Our result builds upon an analysis for linear stochastic approximation based on Lyapunov equations and applies to both tabular setting and with linear function approximation, provided that the optimal policy is unique and the algorithms converge. We show that the asymptotic mean-squared error of Double Q-learning is exactly equal to that of Q-learning if Double Q-learning uses twice the learning rate of Q-learning and outputs the average of its two estimators. We also present some practical implications of this theoretical observation using simulations.
Effectively leveraging large, previously collected datasets in reinforcement learning (RL) is a key challenge for large-scale real-world applications. Offline RL algorithms promise to learn effective policies from previously-collected, static datasets without further interaction. However, in practice, offline RL presents a major challenge, and standard off-policy RL methods can fail due to overestimation of values induced by the distributional shift between the dataset and the learned policy, especially when training on complex and multi-modal data distributions. In this paper, we propose conservative Q-learning (CQL), which aims to address these limitations by learning a conservative Q-function such that the expected value of a policy under this Q-function lower-bounds its true value. We theoretically show that CQL produces a lower bound on the value of the current policy and that it can be incorporated into a policy learning procedure with theoretical improvement guarantees. In practice, CQL augments the standard Bellman error objective with a simple Q-value regularizer which is straightforward to implement on top of existing deep Q-learning and actor-critic implementations. On both discrete and continuous control domains, we show that CQL substantially outperforms existing offline RL methods, often learning policies that attain 2-5 times higher final return, especially when learning from complex and multi-modal data distributions.
We introduce Search with Amortized Value Estimates (SAVE), an approach for combining model-free Q-learning with model-based Monte-Carlo Tree Search (MCTS). In SAVE, a learned prior over state-action values is used to guide MCTS, which estimates an improved set of state-action values. The new Q-estimates are then used in combination with real experience to update the prior. This effectively amortizes the value computation performed by MCTS, resulting in a cooperative relationship between model-free learning and model-based search. SAVE can be implemented on top of any Q-learning agent with access to a model, which we demonstrate by incorporating it into agents that perform challenging physical reasoning tasks and Atari. SAVE consistently achieves higher rewards with fewer training steps, and---in contrast to typical model-based search approaches---yields strong performance with very small search budgets. By combining real experience with information computed during search, SAVE demonstrates that it is possible to improve on both the performance of model-free learning and the computational cost of planning.
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