No Arabic abstract
Probabilistic software analysis aims at quantifying the probability of a target event occurring during the execution of a program processing uncertain incoming data or written itself using probabilistic programming constructs. Recent techniques combine symbolic execution with model counting or solution space quantification methods to obtain accurate estimates of the occurrence probability of rare target events, such as failures in a mission-critical system. However, they face several scalability and applicability limitations when analyzing software processing with high-dimensional and correlated multivariate input distributions. In this paper, we present SYMbolic Parallel Adaptive Importance Sampling (SYMPAIS), a new inference method tailored to analyze path conditions generated from the symbolic execution of programs with high-dimensional, correlated input distributions. SYMPAIS combines results from importance sampling and constraint solving to produce accurate estimates of the satisfaction probability for a broad class of constraints that cannot be analyzed by current solution space quantification methods. We demonstrate SYMPAISs generality and performance compared with state-of-the-art alternatives on a set of problems from different application domains.
The evaluation of rare but high-stakes events remains one of the main difficulties in obtaining reliable policies from intelligent agents, especially in large or continuous state/action spaces where limited scalability enforces the use of a prohibitively large number of testing iterations. On the other hand, a biased or inaccurate policy evaluation in a safety-critical system could potentially cause unexpected catastrophic failures during deployment. In this paper, we propose the Accelerated Policy Evaluation (APE) method, which simultaneously uncovers rare events and estimates the rare event probability in Markov decision processes. The APE method treats the environment nature as an adversarial agent and learns towards, through adaptive importance sampling, the zero-variance sampling distribution for the policy evaluation. Moreover, APE is scalable to large discrete or continuous spaces by incorporating function approximators. We investigate the convergence properties of proposed algorithms under suitable regularity conditions. Our empirical studies show that APE estimates rare event probability with a smaller variance while only using orders of magnitude fewer samples compared to baseline methods in both multi-agent and single-agent environments.
The goal of program synthesis is to automatically generate programs in a particular language from corresponding specifications, e.g. input-output behavior. Many current approaches achieve impressive results after training on randomly generated I/O examples in limited domain-specific languages (DSLs), as with string transformations in RobustFill. However, we empirically discover that applying test input generation techniques for languages with control flow and rich input space causes deep networks to generalize poorly to certain data distributions; to correct this, we propose a new methodology for controlling and evaluating the bias of synthetic data distributions over both programs and specifications. We demonstrate, using the Karel DSL and a small Calculator DSL, that training deep networks on these distributions leads to improved cross-distribution generalization performance.
Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive, we mean that our selection rules are based on the dual residual or the primal-dual gap estimates and can change at each iteration. We theoretically characterize the performance of our selection rules and demonstrate improvements over the state-of-the-art, and extend our theory and algorithms to general convex objectives. Numerical evidence with hinge-loss support vector machines and Lasso confirm that the practice follows the theory.
Reducing the variance of the gradient estimator is known to improve the convergence rate of stochastic gradient-based optimization and sampling algorithms. One way of achieving variance reduction is to design importance sampling strategies. Recently, the problem of designing such schemes was formulated as an online learning problem with bandit feedback, and algorithms with sub-linear static regret were designed. In this work, we build on this framework and propose Avare, a simple and efficient algorithm for adaptive importance sampling for finite-sum optimization and sampling with decreasing step-sizes. Under standard technical conditions, we show that Avare achieves $mathcal{O}(T^{2/3})$ and $mathcal{O}(T^{5/6})$ dynamic regret for SGD and SGLD respectively when run with $mathcal{O}(1/t)$ step sizes. We achieve this dynamic regret bound by leveraging our knowledge of the dynamics defined by the algorithm, and combining ideas from online learning and variance-reduced stochastic optimization. We validate empirically the performance of our algorithm and identify settings in which it leads to significant improvements.
The Adaptive Multiple Importance Sampling (AMIS) algorithm is aimed at an optimal recycling of past simulations in an iterated importance sampling scheme. The difference with earlier adaptive importance sampling implementations like Population Monte Carlo is that the importance weights of all simulated values, past as well as present, are recomputed at each iteration, following the technique of the deterministic multiple mixture estimator of Owen and Zhou (2000). Although the convergence properties of the algorithm cannot be fully investigated, we demonstrate through a challenging banana shape target distribution and a population genetics example that the improvement brought by this technique is substantial.