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Learning to Utilize Shaping Rewards: A New Approach of Reward Shaping

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 Added by Weixun Wang
 Publication date 2020
and research's language is English




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Reward shaping is an effective technique for incorporating domain knowledge into reinforcement learning (RL). Existing approaches such as potential-based reward shaping normally make full use of a given shaping reward function. However, since the transformation of human knowledge into numeric reward values is often imperfect due to reasons such as human cognitive bias, completely utilizing the shaping reward function may fail to improve the performance of RL algorithms. In this paper, we consider the problem of adaptively utilizing a given shaping reward function. We formulate the utilization of shaping rewards as a bi-level optimization problem, where the lower level is to optimize policy using the shaping rewards and the upper level is to optimize a parameterized shaping weight function for true reward maximization. We formally derive the gradient of the expected true reward with respect to the shaping weight function parameters and accordingly propose three learning algorithms based on different assumptions. Experiments in sparse-reward cartpole and MuJoCo environments show that our algorithms can fully exploit beneficial shaping rewards, and meanwhile ignore unbeneficial shaping rewards or even transform them into beneficial ones.



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Learning to solve sparse-reward reinforcement learning problems is difficult, due to the lack of guidance towards the goal. But in some problems, prior knowledge can be used to augment the learning process. Reward shaping is a way to incorporate prior knowledge into the original reward function in order to speed up the learning. While previous work has investigated the use of expert knowledge to generate potential functions, in this work, we study whether we can use a search algorithm(A*) to automatically generate a potential function for reward shaping in Sokoban, a well-known planning task. The results showed that learning with shaped reward function is faster than learning from scratch. Our results indicate that distance functions could be a suitable function for Sokoban. This work demonstrates the possibility of solving multiple instances with the help of reward shaping. The result can be compressed into a single policy, which can be seen as the first phrase towards training a general policy that is able to solve unseen instances.
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Recently, successful approaches have been made to exploit good-for-MDPs automata (Buchi automata with a restricted form of nondeterminism) for model free reinforcement learning, a class of automata that subsumes good for games automata and the most widespread class of limit deterministic automata. The foundation of using these Buchi automata is that the Buchi condition can, for good-for-MDP automata, be translated to reachability. The drawback of this translation is that the rewards are, on average, reaped very late, which requires long episodes during the learning process. We devise a new reward shaping approach that overcomes this issue. We show that the resulting model is equivalent to a discounted payoff objective with a biased discount that simplifies and improves on prior work in this direction.
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64 - Yongle Luo , Kun Dong , Lili Zhao 2020
Efficient and effective learning is one of the ultimate goals of the deep reinforcement learning (DRL), although the compromise has been made in most of the time, especially for the application of robot manipulations. Learning is always expensive for robot manipulation tasks and the learning effectiveness could be affected by the system uncertainty. In order to solve above challenges, in this study, we proposed a simple but powerful reward shaping method, namely Dense2Sparse. It combines the advantage of fast convergence of dense reward and the noise isolation of the sparse reward, to achieve a balance between learning efficiency and effectiveness, which makes it suitable for robot manipulation tasks. We evaluated our Dense2Sparse method with a series of ablation experiments using the state representation model with system uncertainty. The experiment results show that the Dense2Sparse method obtained higher expected reward compared with the ones using standalone dense reward or sparse reward, and it also has a superior tolerance of system uncertainty.
Cooperative game is a critical research area in the multi-agent reinforcement learning (MARL). Global reward game is a subclass of cooperative games, where all agents aim to maximize the global reward. Credit assignment is an important problem studied in the global reward game. Most of previous works stood by the view of non-cooperative-game theoretical framework with the shared reward approach, i.e., each agent being assigned a shared global reward directly. This, however, may give each agent an inaccurate reward on its contribution to the group, which could cause inefficient learning. To deal with this problem, we i) introduce a cooperative-game theoretical framework called extended convex game (ECG) that is a superset of global reward game, and ii) propose a local reward approach called Shapley Q-value. Shapley Q-value is able to distribute the global reward, reflecting each agents own contribution in contrast to the shared reward approach. Moreover, we derive an MARL algorithm called Shapley Q-value deep deterministic policy gradient (SQDDPG), using Shapley Q-value as the critic for each agent. We evaluate SQDDPG on Cooperative Navigation, Prey-and-Predator and Traffic Junction, compared with the state-of-the-art algorithms, e.g., MADDPG, COMA, Independent DDPG and Independent A2C. In the experiments, SQDDPG shows a significant improvement on the convergence rate. Finally, we plot Shapley Q-value and validate the property of fair credit assignment.

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