Bandit Algorithms for Tree Search

Bandit based methods for tree search have recently gained popularity when applied to huge trees, e.g. in the game of go (Gelly et al., 2006). The UCT algorithm (Kocsis and Szepesvari, 2006), a tree search method based on Upper Confidence Bounds (UCB) (Auer et al., 2002), is believed to adapt locally to the effective smoothness of the tree. However, we show that UCT is too ``optimistic'' in some cases, leading to a regret O(exp(exp(D))) where D is the depth of the tree. We propose alternative bandit algorithms for tree search. First, a modification of UCT using a confidence sequence that scales exponentially with the horizon depth is proven to have a regret O(2^D \sqrt{n}), but does not adapt to possible smoothness in the tree. We then analyze Flat-UCB performed on the leaves and provide a finite regret bound with high probability. Then, we introduce a UCB-based Bandit Algorithm for Smooth Trees which takes into account actual smoothness of the rewards for performing efficient ``cuts'' of sub-optimal branches with high confidence. Finally, we present an incremental tree search version which applies when the full tree is too big (possibly infinite) to be entirely represented and show that with high probability, essentially only the optimal branches is indefinitely developed. We illustrate these methods on a global optimization problem of a Lipschitz function, given noisy data

Finite Domain Bounds Consistency Revisited

A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with constraint propagation for pruning the search space. Constraint propagation is performed by propagators implementing a certain notion of consistency. Bounds consistency is the method of choice for building propagators for arithmetic constraints and several global constraints in the finite integer domain. However, there has been some confusion in the definition of bounds consistency. In this paper we clarify the differences and similarities among the three commonly used notions of bounds consistency.Comment: 12 page

Neural Architecture Search using Deep Neural Networks and Monte Carlo Tree Search

Neural Architecture Search (NAS) has shown great success in automating the design of neural networks, but the prohibitive amount of computations behind current NAS methods requires further investigations in improving the sample efficiency and the network evaluation cost to get better results in a shorter time. In this paper, we present a novel scalable Monte Carlo Tree Search (MCTS) based NAS agent, named AlphaX, to tackle these two aspects. AlphaX improves the search efficiency by adaptively balancing the exploration and exploitation at the state level, and by a Meta-Deep Neural Network (DNN) to predict network accuracies for biasing the search toward a promising region. To amortize the network evaluation cost, AlphaX accelerates MCTS rollouts with a distributed design and reduces the number of epochs in evaluating a network by transfer learning, which is guided with the tree structure in MCTS. In 12 GPU days and 1000 samples, AlphaX found an architecture that reaches 97.84\% top-1 accuracy on CIFAR-10, and 75.5\% top-1 accuracy on ImageNet, exceeding SOTA NAS methods in both the accuracy and sampling efficiency. Particularly, we also evaluate AlphaX on NASBench-101, a large scale NAS dataset; AlphaX is 3x and 2.8x more sample efficient than Random Search and Regularized Evolution in finding the global optimum. Finally, we show the searched architecture improves a variety of vision applications from Neural Style Transfer, to Image Captioning and Object Detection.Comment: To appear in the Thirty-Fourth AAAI conference on Artificial Intelligence (AAAI-2020