We introduce a new formulation of the Hidden Parameter Markov Decision Process (HiP-MDP), a framework for modeling families of related tasks using low-dimensional latent embeddings. We also replace the original Gaussian Process-based model with a Bayesian Neural Network, enabling more scalable inference. Thus, we expand the scope of the HiP-MDP to applications with higher dimensions and more complex dynamics. Papers published at the Neural Information Processing Systems Conference.

We study the problem of online learning Markov Decision Processes (MDPs) when both the transition distributions and loss functions are chosen by an adversary. We present an algorithm that, under a mixing assumption, achieves $O(\sqrt{T\log \Pi } \log \Pi)$ regret with respect to a comparison set of policies $\Pi$. The regret is independent of the size of the state and action spaces. When expectations over sample paths can be computed efficiently and the comparison set $\Pi$ has polynomial size, this algorithm is efficient. We also consider the episodic adversarial online shortest path problem.

This paper addresses the problem of online planning in Markov Decision Processes using only a generative model. We propose a new algorithm which is based on the construction of a forest of single successor state planning trees. For every explored state-action, such a tree contains exactly one successor state, drawn from the generative model. The trees are built using a planning algorithm which follows the optimism in the face of uncertainty principle, in assuming the most favorable outcome in the absence of further information. In the decision making step of the algorithm, the individual trees are combined.

Small-variance asymptotics provide an emerging technique for obtaining scalable combinatorial algorithms from rich probabilistic models. We present a small-variance asymptotic analysis of the Hidden Markov Model and its infinite-state Bayesian nonparametric extension. Starting with the standard HMM, we first derive a "hard" inference algorithm analogous to k-means that arises when particular variances in the model tend to zero. This analysis is then extended to the Bayesian nonparametric case, yielding a simple, scalable, and flexible algorithm for discrete-state sequence data with a non-fixed number of states. We also derive the corresponding combinatorial objective functions arising from our analysis, which involve a k-means-like term along with penalties based on state transitions and the number of states.

For spiking neurons, the entropy rate places an upper bound on the rate at which the spike train can convey stimulus information, and a large literature has focused on the problem of estimating entropy rate from spike train data. Our estimator leverages the fact that the entropy rate of an ergodic Markov Chain with known transition probabilities can be calculated analytically, and many stochastic processes that are non-Markovian can still be well approximated by Markov processes of sufficient depth. Choosing an appropriate depth of Markov model presents challenges due to possibly long time dependencies and short data sequences: a deeper model can better account for long time-dependencies, but is more difficult to infer from limited data. Our approach mitigates this difficulty by using a hierarchical prior to share statistical power across Markov chains of different depths. We present both a fully Bayesian and empirical Bayes entropy rate estimator based on this model, and demonstrate their performance on simulated and real neural spike train data.

POMDPs provide a principled framework for planning under uncertainty, but are computationally intractable, due to the "curse of dimensionality" and the "curse of history". This paper presents an online lookahead search algorithm that alleviates these difficulties by limiting the search to a set of sampled scenarios. The execution of all policies on the sampled scenarios is summarized using a Determinized Sparse Partially Observable Tree (DESPOT), which is a sparsely sampled belief tree. Our algorithm, named Regularized DESPOT (R-DESPOT), searches the DESPOT for a policy that optimally balances the size of the policy and the accuracy on its value estimate obtained through sampling. We give an output-sensitive performance bound for all policies derived from the DESPOT, and show that R-DESPOT works well if a small optimal policy exists.

The Markov chain is a convenient tool to represent the dynamics of complex systems such as traffic and social systems, where probabilistic transition takes place between internal states. A Markov chain is characterized by initial-state probabilities and a state-transition probability matrix. In the traditional setting, a major goal is to figure out properties of a Markov chain when those probabilities are known. This paper tackles an inverse version of the problem: we find those probabilities from partial observations at a limited number of states. The observations include the frequency of visiting a state and the rate of reaching a state from another.

In many applications such as advertisement placement or automated dialog systems, an intelligent system optimizes performance over a sequence of interactions with each user. Such tasks often involve many states and potentially time-dependent transition dynamics, and can be modeled well as episodic Markov decision processes (MDPs). In this paper, we present a PAC algorithm for reinforcement learning in episodic finite MDPs with time-dependent transitions that acts epsilon-optimal in all but O(S A H 3 / epsilon 2 log(1 / delta)) episodes. Our algorithm has a polynomial computational complexity, and our sample complexity bound accounts for the fact that we may only be able to approximately solve the internal planning problems. In addition, our PAC sample complexity bound has only linear dependency on the number of states S and actions A and strictly improves previous bounds with S 2 dependency in this setting.

Interactive partially observable Markov decision processes (I-POMDPs) provide a principled framework for planning and acting in a partially observable, stochastic and multi-agent environment. It extends POMDPs to multi-agent settings by including models of other agents in the state space and forming a hierarchical belief structure. In order to predict other agents' actions using I-POMDPs, we propose an approach that effectively uses Bayesian inference and sequential Monte Carlo sampling to learn others' intentional models which ascribe to them beliefs, preferences and rationality in action selection. Empirical results show that our algorithm accurately learns models of the other agent and has superior performance than methods that use subintentional models. Our approach serves as a generalized Bayesian learning algorithm that learns other agents' beliefs, strategy levels, and transition, observation and reward functions. Papers published at the Neural Information Processing Systems Conference.

Relational data--like graphs, networks, and matrices--is often dynamic, where the relational structure evolves over time. A fundamental problem in the analysis of time-varying network data is to extract a summary of the common structure and the dynamics of underlying relations between entities. Here we build on the intuition that changes in the network structure are driven by the dynamics at the level of groups of nodes. We propose a nonparametric multi-group membership model for dynamic networks. Our model contains three main components.