34,908 research outputs found
Monte Carlo Tree Search with Heuristic Evaluations using Implicit Minimax Backups
Monte Carlo Tree Search (MCTS) has improved the performance of game engines
in domains such as Go, Hex, and general game playing. MCTS has been shown to
outperform classic alpha-beta search in games where good heuristic evaluations
are difficult to obtain. In recent years, combining ideas from traditional
minimax search in MCTS has been shown to be advantageous in some domains, such
as Lines of Action, Amazons, and Breakthrough. In this paper, we propose a new
way to use heuristic evaluations to guide the MCTS search by storing the two
sources of information, estimated win rates and heuristic evaluations,
separately. Rather than using the heuristic evaluations to replace the
playouts, our technique backs them up implicitly during the MCTS simulations.
These minimax values are then used to guide future simulations. We show that
using implicit minimax backups leads to stronger play performance in Kalah,
Breakthrough, and Lines of Action.Comment: 24 pages, 7 figures, 9 tables, expanded version of paper presented at
IEEE Conference on Computational Intelligence and Games (CIG) 2014 conferenc
A Survey of Monte Carlo Tree Search Methods
Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work
Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games using Baselines
Learning strategies for imperfect information games from samples of
interaction is a challenging problem. A common method for this setting, Monte
Carlo Counterfactual Regret Minimization (MCCFR), can have slow long-term
convergence rates due to high variance. In this paper, we introduce a variance
reduction technique (VR-MCCFR) that applies to any sampling variant of MCCFR.
Using this technique, per-iteration estimated values and updates are
reformulated as a function of sampled values and state-action baselines,
similar to their use in policy gradient reinforcement learning. The new
formulation allows estimates to be bootstrapped from other estimates within the
same episode, propagating the benefits of baselines along the sampled
trajectory; the estimates remain unbiased even when bootstrapping from other
estimates. Finally, we show that given a perfect baseline, the variance of the
value estimates can be reduced to zero. Experimental evaluation shows that
VR-MCCFR brings an order of magnitude speedup, while the empirical variance
decreases by three orders of magnitude. The decreased variance allows for the
first time CFR+ to be used with sampling, increasing the speedup to two orders
of magnitude
Thinking Fast and Slow with Deep Learning and Tree Search
Sequential decision making problems, such as structured prediction, robotic
control, and game playing, require a combination of planning policies and
generalisation of those plans. In this paper, we present Expert Iteration
(ExIt), a novel reinforcement learning algorithm which decomposes the problem
into separate planning and generalisation tasks. Planning new policies is
performed by tree search, while a deep neural network generalises those plans.
Subsequently, tree search is improved by using the neural network policy to
guide search, increasing the strength of new plans. In contrast, standard deep
Reinforcement Learning algorithms rely on a neural network not only to
generalise plans, but to discover them too. We show that ExIt outperforms
REINFORCE for training a neural network to play the board game Hex, and our
final tree search agent, trained tabula rasa, defeats MoHex 1.0, the most
recent Olympiad Champion player to be publicly released.Comment: v1 to v2: - Add a value function in MCTS - Some MCTS hyper-parameters
changed - Repetition of experiments: improved accuracy and errors shown.
(note the reduction in effect size for the tpt/cat experiment) - Results from
a longer training run, including changes in expert strength in training -
Comparison to MoHex. v3: clarify independence of ExIt and AG0. v4: see
appendix
Learning Policies from Self-Play with Policy Gradients and MCTS Value Estimates
In recent years, state-of-the-art game-playing agents often involve policies
that are trained in self-playing processes where Monte Carlo tree search (MCTS)
algorithms and trained policies iteratively improve each other. The strongest
results have been obtained when policies are trained to mimic the search
behaviour of MCTS by minimising a cross-entropy loss. Because MCTS, by design,
includes an element of exploration, policies trained in this manner are also
likely to exhibit a similar extent of exploration. In this paper, we are
interested in learning policies for a project with future goals including the
extraction of interpretable strategies, rather than state-of-the-art
game-playing performance. For these goals, we argue that such an extent of
exploration is undesirable, and we propose a novel objective function for
training policies that are not exploratory. We derive a policy gradient
expression for maximising this objective function, which can be estimated using
MCTS value estimates, rather than MCTS visit counts. We empirically evaluate
various properties of resulting policies, in a variety of board games.Comment: Accepted at the IEEE Conference on Games (CoG) 201
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