This paper addresses the problem of learning a task from demonstration. We adopt the framework of inverse reinforcement learning, where tasks are represented in the form of a reward function. Our contribution is a novel active learning algorithm that enables the learning agent to query the expert for more informative demonstrations, thus leading to more sample-efficient learning. For this novel algorithm (Generalized Binary Search for Inverse Reinforcement Learning, or GBS-IRL), we provide a theoretical bound on sample complexity and illustrate its applicability on several different tasks. To our knowledge, GBS-IRL is the first active IRL algorithm with provable sample complexity bounds. We also discuss our method in light of other existing methods in the literature and its general applicability in multi-class classification problems. Finally, motivated by recent work on learning from demonstration in robots, we also discuss how different forms of human feedback can be integrated in a transparent manner in our learning framework.
@cite_8 introduced (BIRL), where the IRL problem is cast as a Bayesian inference problem. Given a prior distribution over possible target tasks, the algorithm uses the demonstration by the expert as evidence to compute the posterior distribution over tasks and identify the target task. Unfortunately, the Monte-Carlo Markov chain (MCMC) algorithm used to approximate the posterior distribution is computationally expensive, as it requires extensive sampling of the space of possible rewards. To avoid such complexity, several posterior works have departed from the BIRL formulation and instead determine the task that maximizes the likelihood of the observed demonstration .
@cite_8
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Tasks such as record linkage and multi-target tracking, which involve reconstructing the set of objects that underlie some observed data, are particularly challenging for probabilistic inference. Recent work has achieved efficient and accurate inference on such problems using Markov chain Monte Carlo (MCMC) techniques with customized proposal distributions. Currently, implementing such a system requires coding MCMC state representations and acceptance probability calculations that are specific to a particular application. An alternative approach, which we pursue in this paper, is to use a general-purpose probabilistic modeling language (such as BLOG) and a generic Metropolis-Hastings MCMC algorithm that supports user-supplied proposal distributions. Our algorithm gains flexibility by using MCMC states that are only partial descriptions of possible worlds; we provide conditions under which MCMC over partial worlds yields correct answers to queries. We also show how to use a context-specific Bayes net to identify the factors in the acceptance probability that need to be computed for a given proposed move. Experimental results on a citation matching task show that our general-purpose MCMC engine compares favorably with an application-specific system. Stimulus reconstruction or decoding methods provide an important tool for understanding how sensory and motor information is represented in neural activity. We discuss Bayesian decoding methods based on an encoding generalized linear model (GLM) that accurately describes how stimuli are transformed into the spike trains of a group of neurons. The form of the GLM likelihood ensures that the posterior distribution over the stimuli that caused an observed set of spike trains is log concave so long as the prior is. This allows the maximum a posteriori (MAP) stimulus estimate to be obtained using efficient optimization algorithms. Unfortunately, the MAP estimate can have a relatively large average error when the posterior is highly nongaussian. Here we compare several Markov chain Monte Carlo (MCMC) algorithms that allow for the calculation of general Bayesian estimators involving posterior expectations (conditional on model parameters). An efficient version of the hybrid Monte Carlo (HMC) algorithm was significantly superior to other MCMC methods for gaussian priors. When the prior distribution has sharp edges and corners, on the other hand, the “hit-and-run” algorithm performed better than other MCMC methods. Using these algorithms, we show that for this latter class of priors, the posterior mean estimate can have a considerably lower average error than MAP, whereas for gaussian priors, the two estimators have roughly equal efficiency. We also address the application of MCMC methods for extracting nonmarginal properties of the posterior distribution. For example, by using MCMC to calculate the mutual information between the stimulus and response, we verify the validity of a computationally efficient Laplace approximation to this quantity for gaussian priors in a wide range of model parameters; this makes direct model-based computation of the mutual information tractable even in the case of large observed neural populations, where methods based on binning the spike train fail. Finally, we consider the effect of uncertainty in the GLM parameters on the posterior estimators. We present a new Markov Chain Monte Carlo (MCMC) sampling algorithm for probabilistic programs. Our approach and tool, called R2, has the unique feature of employing program analysis in order to improve the efficiency of MCMC sampling. Given an input program P, R2 propagates observations in P backwards to obtain a semantically equivalent program P′ in which every probabilistic assignment is immediately followed by an observe statement. Inference is performed by a suitably modified version of the Metropolis-Hastings algorithm that exploits the structure of the program P′. This has the overall effect of preventing rejections due to program executions that fail to satisfy observations in P. We formalize the semantics of probabilistic programs and rigorously prove the correctness of R2. We also empirically demonstrate the effectiveness of R2--in particular, we show that R2 is able to produce results of similar quality as the CHURCH and STAN probabilistic programming tools with much shorter execution time. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have non-negligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior “landscape”. We present empirical results on synthetic and real-life datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a non-Bayesian bootstrap approach.