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

Trial-based Heuristic Tree Search for MDPs with Factored Action Spaces

MDPs with factored action spaces, i.e. where actions are described as assignments to a set of action variables, allow reasoning over action variables instead of action states, yet most algorithms only consider a grounded action representation. This includes algorithms that are instantiations of the trial-based heuristic tree search (THTS) framework, such as AO* or UCT. To be able to reason over factored action spaces, we propose a generalisation of THTS where nodes that branch over all applicable actions are replaced with subtrees that consist of nodes that represent the decision for a single action variable. We show that many THTS algorithms retain their theoretical properties under the generalised framework, and show how to approximate any state-action heuristic to a heuristic for partial action assignments. This allows to guide a UCT variant that is able to create exponentially fewer nodes than the same algorithm that considers ground actions. An empirical evaluation on the benchmark set of the probabilistic track of the latest International Planning Competition validates the benefits of the approach

Understanding and Improving Continuous Experimentation : From A/B Testing to Continuous Software Optimization

Controlled experiments (i.e. A/B tests) are used by many companies with user-intensive products to improve their software with user data. Some companies adopt an experiment-driven approach to software development with continuous experimentation (CE). With CE, every user-affecting software change is evaluated in an experiment and specialized roles seek out opportunities to experiment with functionality. The goal of the thesis is to describe current practice and support CE in industry. The main contributions are threefold. First, a review of the CE literature on: infrastructure and processes, the problem-solution pairs applied in industry practice, and the benefits and challenges of the practice. Second, a multi-case study with 12 companies to analyze how experimentation is used and why some companies fail to fully realize the benefits of CE. A theory for Factors Affecting Continuous Experimentation (FACE) is constructed to realize this goal. Finally, a toolkit called Constraint Oriented Multi-variate Bandit Optimization (COMBO) is developed for supporting automated experimentation with many variables simultaneously, live in a production environment.The research in the thesis is conducted under the design science paradigm using empirical research methods, with simulation experiments of tool proposals and a multi-case study on company usage of CE. Other research methods include systematic literature review and theory building.From FACE we derive three factors that explain CE utility: (1) investments in data infrastructure, (2) user problem complexity, and (3) incentive structures for experimentation. Guidelines are provided on how to strive towards state-of-the-art CE based on company factors. All three factors are relevant for companies wanting to use CE, in particular, for those companies wanting to apply algorithms such as those in COMBO to support personalization of software to users' context in a process of continuous optimization

Sample-based Search Methods for Bayes-Adaptive Planning

A fundamental issue for control is acting in the face of uncertainty about the environment. Amongst other things, this induces a trade-off between exploration and exploitation. A model-based Bayesian agent optimizes its return by maintaining a posterior distribution over possible environments, and considering all possible future paths. This optimization is equivalent to solving a Markov Decision Process (MDP) whose hyperstate comprises the agent's beliefs about the environment, as well as its current state in that environment. This corresponding process is called a Bayes-Adaptive MDP (BAMDP). Even for MDPs with only a few states, it is generally intractable to solve the corresponding BAMDP exactly. Various heuristics have been devised, but those that are computationally tractable often perform indifferently, whereas those that perform well are typically so expensive as to be applicable only in small domains with limited structure. Here, we develop new tractable methods for planning in BAMDPs based on recent advances in the solution to large MDPs and general partially observable MDPs. Our algorithms are sample-based, plan online in a way that is focused on the current belief, and, critically, avoid expensive belief updates during simulations. In discrete domains, we use Monte-Carlo tree search to search forward in an aggressive manner. The derived algorithm can scale to large MDPs and provably converges to the Bayes-optimal solution asymptotically. We then consider a more general class of simulation-based methods in which approximation methods can be employed to allow value function estimates to generalize between hyperstates during search. This allows us to tackle continuous domains. We validate our approach empirically in standard domains by comparison with existing approximations. Finally, we explore Bayes-adaptive planning in environments that are modelled by rich, non-parametric probabilistic models. We demonstrate that a fully Bayesian agent can be advantageous in the exploration of complex and even infinite, structured domains