An Information-Theoretic Analysis of Thompson Sampling

We provide an information-theoretic analysis of Thompson sampling that applies across a broad range of online optimization problems in which a decision-maker must learn from partial feedback. This analysis inherits the simplicity and elegance of information theory and leads to regret bounds that scale with the entropy of the optimal-action distribution. This strengthens preexisting results and yields new insight into how information improves performance

Cover Tree Bayesian Reinforcement Learning

This paper proposes an online tree-based Bayesian approach for reinforcement learning. For inference, we employ a generalised context tree model. This defines a distribution on multivariate Gaussian piecewise-linear models, which can be updated in closed form. The tree structure itself is constructed using the cover tree method, which remains efficient in high dimensional spaces. We combine the model with Thompson sampling and approximate dynamic programming to obtain effective exploration policies in unknown environments. The flexibility and computational simplicity of the model render it suitable for many reinforcement learning problems in continuous state spaces. We demonstrate this in an experimental comparison with least squares policy iteration

Perturbed-History Exploration in Stochastic Linear Bandits

We propose a new online algorithm for minimizing the cumulative regret in stochastic linear bandits. The key idea is to build a perturbed history, which mixes the history of observed rewards with a pseudo-history of randomly generated i.i.d. pseudo-rewards. Our algorithm, perturbed-history exploration in a linear bandit (LinPHE), estimates a linear model from its perturbed history and pulls the arm with the highest value under that model. We prove a $\tilde{O}(d \sqrt{n})$ gap-free bound on the expected $n$-round regret of LinPHE, where $d$ is the number of features. Our analysis relies on novel concentration and anti-concentration bounds on the weighted sum of Bernoulli random variables. To show the generality of our design, we extend LinPHE to a logistic reward model. We evaluate both algorithms empirically and show that they are practical

Seamlessly Unifying Attributes and Items: Conversational Recommendation for Cold-Start Users

Static recommendation methods like collaborative filtering suffer from the inherent limitation of performing real-time personalization for cold-start users. Online recommendation, e.g., multi-armed bandit approach, addresses this limitation by interactively exploring user preference online and pursuing the exploration-exploitation (EE) trade-off. However, existing bandit-based methods model recommendation actions homogeneously. Specifically, they only consider the items as the arms, being incapable of handling the item attributes, which naturally provide interpretable information of user's current demands and can effectively filter out undesired items. In this work, we consider the conversational recommendation for cold-start users, where a system can both ask the attributes from and recommend items to a user interactively. This important scenario was studied in a recent work. However, it employs a hand-crafted function to decide when to ask attributes or make recommendations. Such separate modeling of attributes and items makes the effectiveness of the system highly rely on the choice of the hand-crafted function, thus introducing fragility to the system. To address this limitation, we seamlessly unify attributes and items in the same arm space and achieve their EE trade-offs automatically using the framework of Thompson Sampling. Our Conversational Thompson Sampling (ConTS) model holistically solves all questions in conversational recommendation by choosing the arm with the maximal reward to play. Extensive experiments on three benchmark datasets show that ConTS outperforms the state-of-the-art methods Conversational UCB (ConUCB) and Estimation-Action-Reflection model in both metrics of success rate and average number of conversation turns.Comment: TOIS 202