Stochastic Gradient Bayesian Optimal Experimental Designs for Simulation-based Inference

Simulation-based inference (SBI) methods tackle complex scientific models with challenging inverse problems. However, SBI models often face a significant hurdle due to their non-differentiable nature, which hampers the use of gradient-based optimization techniques. Bayesian Optimal Experimental Design (BOED) is a powerful approach that aims to make the most efficient use of experimental resources for improved inferences. While stochastic gradient BOED methods have shown promising results in high-dimensional design problems, they have mostly neglected the integration of BOED with SBI due to the difficult non-differentiable property of many SBI simulators. In this work, we establish a crucial connection between ratio-based SBI inference algorithms and stochastic gradient-based variational inference by leveraging mutual information bounds. This connection allows us to extend BOED to SBI applications, enabling the simultaneous optimization of experimental designs and amortized inference functions. We demonstrate our approach on a simple linear model and offer implementation details for practitioners.Comment: Presented at ICML 2023 workshop on Differentiable Everythin

Notes on using simulation-optimization techniques in traffic simulation

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Mathematical and simulation models of systems lay at the core of many decision support systems, and their role becomes more critical when the system is more complex. The decision process usually involves optimizing some utility function that evaluates the performance indicators measuring the impacts of the decisions. The complexity of the system directly increases the difficulty when the associated function to be optimized is a non-analytical, non-differentiable, non-linear function that can only be evaluated by simulation. Simulation-optimization techniques are especially suited to these cases, and its use is becoming increasingly used with traffic models, which represent an archetypal case of complex, dynamic systems that exhibit highly stochastic characteristics. In this approach, simulation is used to evaluate the objective function, and it is combined with a non-differentiable optimization technique for solving the associated optimization problem. Of these techniques, one of the most commonly used is Stochastic Perturbation Stochastic Approximation (SPSA). This paper analyses, discusses and presents the computational results from applying this technique in the calibration of traffic simulation models. This study uses variants of the SPSA by replacing the usual gradient approach with a combination of projected gradient and trust region methods. A special approach has also been analyzed for parameter calibration cases in which each variable has a different magnitude.Peer ReviewedPostprint (published version

Sensitivity Analysis and Discrete Stochastic Optimization for Semiconductor Manufacturing Systems

The semiconductor industry is a capital-intensive industry with rapid time-to-market, short product development cycles, complex product flows and other characteristics. These factors make it necessary to utilize equipment efficiently and reduce cycle times. Further, the complexity and highly stochastic nature of these manufacturing systems make it difficult to study their characteristics through analytical models. Hence we resort to simulation-based methodologies to model these systems.This research aims at developing and implementing simulation-based operations research techniques to facilitate System Control (through sensitivity analysis) and System Design (through optimization) for semiconductor manufacturing systems.Sensitivity analysis for small changes in input parameters is performed using gradient estimation techniques. Gradient estimation methods are evaluated by studying the state of the art and comparing the finite difference method and simultaneous perturbation method by applying them to a stochastic manufacturing system. The results are compared with the gradients obtained through analytical queueing models. The finite difference method is implemented in a heterogeneous simulation environment (HSE)-based decision support tool for process engineers. This tool performs heterogeneous simulations and sensitivity analyses.The gradient-based techniques used for sensitivity analysis form the building blocks for a gradient-based discrete stochastic optimization procedure. This procedure is applied to the problem of allocating a limited budget to machine purchases to achieve throughput requirements and minimize cycle time. The performance of the algorithm is evaluated by applying the algorithm on a wide range of problem instances

Biochemical systems identification by a random drift particle swarm optimization approach

BACKGROUND: Finding an efficient method to solve the parameter estimation problem (inverse problem) for nonlinear biochemical dynamical systems could help promote the functional understanding at the system level for signalling pathways. The problem is stated as a data-driven nonlinear regression problem, which is converted into a nonlinear programming problem with many nonlinear differential and algebraic constraints. Due to the typical ill conditioning and multimodality nature of the problem, it is in general difficult for gradient-based local optimization methods to obtain satisfactory solutions. To surmount this limitation, many stochastic optimization methods have been employed to find the global solution of the problem. RESULTS: This paper presents an effective search strategy for a particle swarm optimization (PSO) algorithm that enhances the ability of the algorithm for estimating the parameters of complex dynamic biochemical pathways. The proposed algorithm is a new variant of random drift particle swarm optimization (RDPSO), which is used to solve the above mentioned inverse problem and compared with other well known stochastic optimization methods. Two case studies on estimating the parameters of two nonlinear biochemical dynamic models have been taken as benchmarks, under both the noise-free and noisy simulation data scenarios. CONCLUSIONS: The experimental results show that the novel variant of RDPSO algorithm is able to successfully solve the problem and obtain solutions of better quality than other global optimization methods used for finding the solution to the inverse problems in this study

Exploiting the Statistics of Learning and Inference

When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by exploiting their inherent statistical nature. We propose algorithms that exploit the redundancy of data relative to a model by subsampling data-cases for every update and reasoning about the uncertainty created in this process. In the context of learning we propose to test for the probability that a stochastically estimated gradient points more than 180 degrees in the wrong direction. In the context of MCMC sampling we use stochastic gradients to improve the efficiency of MCMC updates, and hypothesis tests based on adaptive mini-batches to decide whether to accept or reject a proposed parameter update. Finally, we argue that in the context of likelihood free MCMC one needs to store all the information revealed by all simulations, for instance in a Gaussian process. We conclude that Bayesian methods will remain to play a crucial role in the era of big data and big simulations, but only if we overcome a number of computational challenges.Comment: Proceedings of the NIPS workshop on "Probabilistic Models for Big Data