Value targets in off-policy AlphaZero: a new greedy backup


This article presents and evaluates a family of AlphaZero value targets, subsuming previous variants and introducing AlphaZero with greedy backups (A0GB). Current state-of-the-art algorithms for playing board games use sample-based planning, such as Monte Carlo Tree Search (MCTS), combined with deep neural networks (NN) to approximate the value function. These algorithms, of which AlphaZero is a prominent example, are computationally extremely expensive to train, due to their reliance on many neural network evaluations. This limits their practical performance. We improve the training process of AlphaZero by using more effective training targets for the neural network. We introduce a three-dimensional space to describe a family of training targets, covering the original AlphaZero training target as well as the soft-Z and A0C variants from the literature. We demonstrate that A0GB, using a specific new value target from this family, is able to find the optimal policy in a small tabular domain, whereas the original AlphaZero target fails to do so. In addition, we show that soft-Z, A0C and A0GB achieve better performance and faster training than the original AlphaZero target on two benchmark board games (Connect-Four and Breakthrough). Finally, we juxtapose tabular learning with neural network-based value function approximation in Tic-Tac-Toe, and compare the effects of learning targets therein.

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  1. 1.

    The bias that we talk about here is a different bias than the one associated with the bias-variance trade-off between bootstrapping and Monte Carlo methods. That bias is associated with the (transient) effect of value initialization. The bias we are considering here is permanent and associated with the difference between the actual and ideal target policy.

  2. 2.

    The replay buffer that is used for training the neural network also contains samples that were sampled from older versions of \(\pi _\mathrm{AlphaZero}\). One could argue that this makes AlphaZero off-policy, but we do not go into the details about the effects of replay buffers in this work.


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The authors would like to thank the anonymous reviewers for their constructive feedback, which helped improve the manuscript. This work is part of the project Flexible Assets Bid Across Markets (FABAM, project number TEUE117015), funded within the Dutch Topsector Energie / TKI Urban Energy by Rijksdienst voor Ondernemend Nederland (RvO).

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Correspondence to Daniel Willemsen.

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An abridged version of this work has previously been presented at the Adaptive and Learning Agents workshop at AAMAS 2020 [24]. This extended version introduces additional results and performance analyses on the Tic-Tac-Toe domain.

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Willemsen, D., Baier, H. & Kaisers, M. Value targets in off-policy AlphaZero: a new greedy backup. Neural Comput & Applic (2021).

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  • Reinforcement learning
  • Sample-based planning
  • AlphaZero
  • MCTS