We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors. To express such models, we introduce a probabilistic programming language that supports discrete and continuous sampling, discrete observations, affine functions, (stochastic) branching, and conditioning on discrete events. Our key tool is probability generating functions: they provide a compact closed-form representation of distributions that are definable by programs, thus enabling the exact computation of posterior probabilities, expectation, variance, and higher moments. Our inference method is provably correct and fully automated in a tool called Genfer, which uses automatic differentiation (specifically, Taylor polynomials), but does not require computer algebra. Our experiments show that Genfer is often faster than the existing exact inference tools PSI, Dice, and Prodigy. On a range of real-world inference problems that none of these exact tools can solve, Genfer's performance is competitive with approximate Monte Carlo methods, while avoiding approximation errors.

We study the problem of off-policy evaluation (OPE) for episodic Partially Observable Markov Decision Processes (POMDPs) with continuous states. Motivated by the recently proposed proximal causal inference framework, we develop a non-parametric identification result for estimating the policy value via a sequence of so-called V-bridge functions with the help of time-dependent proxy variables. We then develop a fitted-Q-evaluation-type algorithm to estimate V-bridge functions recursively, where a non-parametric instrumental variable (NPIV) problem is solved at each step. By analyzing this challenging sequential NPIV problem, we establish the finite-sample error bounds for estimating the V-bridge functions and accordingly that for evaluating the policy value, in terms of the sample size, length of horizon and so-called (local) measure of ill-posedness at each step. To the best of our knowledge, this is the first finite-sample error bound for OPE in POMDPs under non-parametric models.

We present a novel actor-critic algorithm for an environment with delayed feedback, which addresses the state-space explosion problem of conventional approaches. Conventional approaches use an augmented state constructed from the last observed state and actions executed since visiting the last observed state Using the augmented state space, the correct Markov decision process for delayed environments can be constructed; however, this causes the state space to explode as the number of delayed timesteps increases, leading to slow convergence. Our proposed algorithm, called Belief-Projection-Based Q-learning (BPQL), addresses the state-space explosion problem by evaluating the values of the critic for which the input state size is equal to the original state-space size rather than that of the augmented one. We compare BPQL to traditional approaches in continuous control tasks and demonstrate that it significantly outperforms other algorithms in terms of asymptotic performance and sample efficiency. We also show that BPQL solves long-delayed environments, which conventional approaches are unable to do.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/