Online Learning of k-CNF Boolean Functions

This paper revisits the problem of learning a k-CNF Boolean function from examples in the context of online learning under the logarithmic loss. In doing so, we give a Bayesian interpretation to one of Valiant's celebrated PAC learning algorithms, which we then build upon to derive two efficient, online, probabilistic, supervised learning algorithms for predicting the output of an unknown k-CNF Boolean function. We analyze the loss of our methods, and show that the cumulative log-loss can be upper bounded, ignoring logarithmic factors, by a polynomial function of the size of each example.Comment: 20 LaTeX pages. 2 Algorithms. Some Theorem

Sparse Sequential Dirichlet Coding

This short paper describes a simple coding technique, Sparse Sequential Dirichlet Coding, for multi-alphabet memoryless sources. It is appropriate in situations where only a small, unknown subset of the possible alphabet symbols can be expected to occur in any particular data sequence. We provide a competitive analysis which shows that the performance of Sparse Sequential Dirichlet Coding will be close to that of a Sequential Dirichlet Coder that knows in advance the exact subset of occurring alphabet symbols. Empirically we show that our technique can perform similarly to the more computationally demanding Sequential Sub-Alphabet Estimator, while using less computational resources.Comment: 7 page

Reinforcement Learning via AIXI Approximation

This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.Comment: 8 LaTeX pages, 1 figur

Approximate universal artificial intelligence and self-play learning for games

This thesis is split into two independent parts. The first is an investigation of some practical aspects of Marcus Hutter's Universal Artificial Intelligence theory. The main contributions are to show how a very general agent can be built and analysed using the mathematical tools of this theory. Before the work presented in this thesis, it was an open question as to whether this theory was of any relevance to reinforcement learning practitioners. This work suggests that it is indeed relevant and worthy of future investigation. The second part of this thesis looks at self-play learning in two player, deterministic, adversarial turn-based games. The main contribution is the introduction of a new technique for training the weights of a heuristic evaluation function from data collected by classical game tree search algorithms. This method is shown to outperform previous self-play training routines based on Temporal Difference learning when applied to the game of Chess. In particular, the main highlight was using this technique to construct a Chess program that learnt to play master level Chess by tuning a set of initially random weights from self play games

Context tree switching

This paper describes the Context Tree Switching technique, a modification of Context Tree Weighting for the prediction of binary, stationary, n-Markov sources. By modifying Context Tree Weighting’s recursive weighting scheme, it is possible to mix over a strictly larger class of models without increasing the asymptotic time or space complexity of the original algorithm. We prove that this generalization preserves the desirable theoretical properties of Context Tree Weighting on stationary n-Markov sources, and show empirically that this new technique leads to consistent improvements over Context Tree Weighting as measured on the Calgary Corpus

Reinforcement Learning via AIXI Approximation

This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains