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Title: Guiding MCTS with Generalized Policies for Probabilistic Planning

Paper content:
We examine techniques for combining generalized policies with search algorithms to exploit the strengths and overcome the weaknesses of each when solving probabilistic planning problems.
The Action Schema Network (ASNet) is a recent contribution to planning that uses deep learning and neural networks to learn generalized policies for probabilistic planning problems.
ASNets are well suited to problems where local knowledge of the environment can be exploited to improve performance, but may fail to generalize to problems they were not trained on.
Monte-Carlo Tree Search (MCTS) is a forward-chaining state space search algorithm for optimal decision making which performs simulations to incrementally build a search tree and estimate the values of each state.
Although MCTS can achieve state-of-the-art results when paired with domain-specific knowledge, without this knowledge, MCTS requires a large number of simulations in order to obtain reliable estimates in the search tree.
By combining ASNets with MCTS, we are able to improve the capability of an ASNet to generalize beyond the distribution of problems it was trained on, as well as enhance the navigation of the search space by MCTS.
Planning is the essential ability of a rational agent to solve the problem of choosing which actions to take in an environment to achieve a certain goal.
This paper is mainly concerned with combining the advantages of forward-chaining state space search through UCT BID11 , an instance of Monte-Carlo Tree Search (MCTS) BID5 , with the domain-specific knowledge learned by Action Schema Networks (ASNets) BID18 ), a domain-independent learning algorithm.
By combining UCT and ASNets, we hope to more effectively solve planning problems, and achieve the best of both worlds.The Action Schema Network (ASNet) is a recent contribution in planning that uses deep learning and neural networks to learn generalized policies for planning problems.
A generalized policy is a policy that can be applied to any problem from a given planning domain.
Ideally, this generalized policy is able to reliably solve all problems in the given domain, although this is not always feasible.
ASNets are well suited to problems where "local knowledge of the environment can help to avoid certain traps" BID18 .
In such problems, an ASNet can significantly outperform traditional planners that use heuristic search.
Moreover, a significant advantage of ASNets is that a network can be trained on a limited number of small problems, and generalize to problems of any size.
However, an ASNet is not guaranteed to reliably solve all problems of a given domain.
For example, an ASNet could fail to generalize to difficult problems that it was not trained on -an issue often encountered with machine learning algorithms.
Moreover, the policy learned by an ASNet could be suboptimal due to a poor choice of hyperparameters that has led to an undertrained or overtrained network.
Although our discussion is closely tied to ASNets, our contributions are more generally applicable to any method of learning a (generalized) policy.Monte-Carlo Tree Search (MCTS) is a state-space search algorithm for optimal decision making which relies on performing Monte-Carlo simulations to build a search tree and estimate the values of each state BID5 ).
As we perform more and more of these simulations, the state estimates become more accurate.
MCTS-based game-playing algorithms have often achieved state-of-the-art performance when paired with domain-specific knowledge, the most notable being AlphaGo (Silver et al. 2016) .
One significant limitation of vanilla MCTS is that we may require a large number of simulations in order to obtain reliable estimates in the search tree.
Moreover, because simulations are random, the search may not be able to sense that certain branches of the tree will lead to sub-optimal outcomes.
We are concerned with UCT, a variant of MCTS that balances the trade-off between exploration and exploitation.
However, our work can be more generally used with other search algorithms.Combining ASNets with UCT achieves three goals.(1
) Learn what we have not learned: improve the capability of an ASNet to generalize beyond the distribution of problems it was trained on, and of UCT to bias the exploration of actions to those that an ASNet wishes to exploit. (
2) Improve on sub-optimal learning: obtain reasonable evaluation-time performance even when an ASNet was trained with suboptimal hyperparameters, and allow UCT to converge to the optimal action in a smaller number of trials.
(3) Be robust to changes in the environment or domain: improve performance when the test environment differs substantially from the training environment.The rest of the paper is organized as follows.
Section 2 formalizes probabilistic planning as solving a Stochastic Shortest Path problem and gives an overview of ASNets and MCTS along with its variants.
Section 3 defines a framework for Dynamic Programming UCT (DP-UCT) BID10 .
Next, Section 4 examines techniques for combining the policy learned by an ASNet with DP-UCT.
Section 5 then presents and analyzes our results.
Finally, Section 6 summarizes our contributions and discusses related and future work.
In this paper, we have investigated techniques to improve search using generalized policies.
We discussed a framework for DP-UCT, extended from THTS, that allowed us to generate different flavors of DP-UCT including those that exploited the generalized policy learned by an ASNet.
We then introduced methods of using this generalized policy in the simulation function, through STOCHASTIC ASNETS and MAXIMUM ASNETS.
These allowed us to obtain more accurate state-value estimates and action-value estimates in the search tree.
We also extended UCB1 to bias the navigation of the search space to the actions that an ASNet wants to exploit whilst maintaining the fundamental balance between exploration and exploitation, by introducing SIMPLE-ASNET and RANKED-ASNET action selection.We have demonstrated through our experiments that our algorithms are capable of improving the capability of an ASNet to generalize beyond the distribution of problems it was trained on, as well as improve sub-optimal learning.
By combining DP-UCT with ASNets, we are able to bias the exploration of actions to those that an ASNet wishes to exploit, and allow DP-UCT to converge to the optimal action in a smaller number of trials.
Our experiments have also demonstrated that by harnessing the power of search, we may overcome any misleading information provided by an ASNet due to a change in the environment.
Hence, we achieved the three following goals: (1) Learn what we have not learned, (2) Improve on sub-optimal learning, and (3) Be robust to changes in the environment or domain.It is important to observe that our contributions are more generally applicable to any method of learning a (generalized) policy (not just ASNets), and potentially to other trialbased search algorithms including (L)RTDP.In the deterministic setting, there has been a long tradition of learning generalized policies and using them to guide heuristic Best First Search (BFS).
For instance, Yoon et al. BID20 add the states resulting from selecting actions prescribed by the learned generalized policy to the the queue of a BFS guided by a relaxed-plan heuristic, and de la BID7 learn and use generalized policies to generate lookahead states within a BFS guided by the FF heuristic.
These authors observe that generalized policies provide effective search guidance, and that search helps correcting deficiencies in the learned policy.
Search control knowledgeà la TLPlan, Talplanner or SHOP2 has been successfully used to prune the search of probabilistic planners BID13 BID17 ).
More recently, BID15 have also experimented with the use of preferred actions in variants of RTDP BID1 and AO* BID14 , albeit with limited success.
Our work differs from these approaches by focusing explicitly on MCTS as the search algorithm and, unlike existing work combining deep learning and MCTS (e.g. AlphaGo (Silver et al. 2016)), looks not only at using neural network policies as a simulation function for rollouts, but also as a means to bias the UCB1 action selection rule.There are still many potential avenues for future work.
We may investigate how to automatically learn the influence parameter M for SIMPLE-ASNET and RANKED-ASNET action selection, or how to combat bad information provided by an ASNet in a simulation function by mixing ASNet simulations with random simulations.
We may also investigate techniques to interleave planning with learning by using UCT with ASNets as a 'teacher' for training an AS

assistant: text: Techniques for combining generalized policies with search algorithms to exploit the strengths and overcome the weaknesses of each when solving probabilistic planning problems