本研究提出新的期望值方法之實務計算方式，應用於強化學習中的價值逼近函數中。減緩同時使用最佳化方法與 ϵ - greedy 策略時，產生的價值高估問題。並將本研究的價值估計方法，應用於優勢學習演算法，提出期望優勢學習演算法。

相較於傳統的 softmax policy 直接使用動作價值計算動作機率分布，本研究使用動作價值的 tanh 數值計算動作機率分布。藉由 tanh 函數限制增長的特性，避免最大動作價值主導動作機率分布，讓產生的動作機率分布不會集中於特定動作。確保使用期望值方法計算價值時，產生的價值不會有嚴重的價值高估情況。

於實驗結果中，本研究以總得分、總步數、平均得分與最高得分四個指標，評估Deep Q Network 演算法、優勢學習演算法、期望優勢學習演算法三者的表現。並於本研究選擇的三個實驗環境中，期望優勢學習皆獲得最高分。透過觀察總得分可以發現，在相同的訓練總次數下，使用期望優勢學習演算法相較於優勢學習演算法，至多增加 6% 的總得分。

In this study, we propose a practical expectation-based value function approximation method to decrease the value overestimation in temporal-difference (TD) learning. Because of Optimizer's Curse, value will be overestimated easily either in softmax policy or greedy policy.

In order to address this problem, we use the tanh value of action-value instead of action-value to calculate policy. Tanh function will limit the extreme and decline the influence of maximal action-value in policy. With this tanh softmax policy, our expectation-based method can decrease the value overestimation successfully.

Examining the benefit of decreasing value overestimation, we corporate our expectation-based method into advantage learning (AL) and propose expected advantage learning (eAL). We use four criteria to evaluate the performance of Deep Q Network (DQN), AL and eAL in every episodes. Our result shows that eAL can improve the performance in score-related criteria, and got maximal 6% more than AL got in the highest score criterion.

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