Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time. This is because the resulting planning task takes the form of a dynamic programming problem on a belief tree with an infinite number of states. The second type employs relatively simple algorithm which are shown to suffer small regret within a distribution-free framework. This paper presents a lower bound and a high probability upper bound on the optimal value function for the nodes in the Bayesian belief tree, which are analogous to similar bounds in POMDPs. The bounds are then used to create more efficient strategies for exploring the tree. The resulting algorithms are compared with the distribution-free algorithm UCB1, as well as a simpler baseline algorithm on multi-armed bandit problems.
The algorithm maintains a surrogate of the unknown function in the form of a random Fourier expansion (RFE). The surrogate is updated whenever a new measurement is available, and then used to determine the next measurement point. The algorithm is comparable to Bayesian optimization algorithms, but its computational complexity per iteration does not depend on the number of measurements. We derive several theoretical results that provide insight on how the hyperparameters of the algorithm should be chosen. The algorithm is compared to a Bayesian optimization algorithm for a benchmark problem and two optics applications, namely, optical coherence tomography and optical beam-forming network tuning.
These challenges can be addressed by enforcing sparsity in the series representation through retaining only the most important basis terms. In this work, we present a novel sparse Bayesian learning technique for obtaining sparse Polynomial Chaos expansions which is based on a Relevance Vector Machine model and is trained using Variational Inference. The methodology shows great potential in high-dimensional data-driven settings using relatively few data points and achieves user-controlled sparse levels that are comparable to other methods such as compressive sensing. The proposed approach is illustrated on two numerical examples, a synthetic response function that is explored for validation purposes and a low-carbon steel plate with random Young's modulus and random loading, which is modelled by stochastic finite element with 38 input random variables.
Multiply sectioned Bayesian networks (MSBNs) provide a general and exact framework for multi-agent distributed interpretation. To investigate algorithms for inference and other operations, experimental MSBNs are necessary. However, it is very time consuming and tedious to construct MSBNs manually. In this work, we investigate pseduo-random generation of MSBNs. Our focus is on the generation of MSBN structures. Pseduo-random generation of MSBN structures can be performed by a generate-and-test approach.
In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in inputs lead to unacceptably large variation in outputs. Our approach uses multiple gradient Gaussian Process models to estimate the probability that worst-case output variation for specified input perturbation exceeded the desired maxima, and these probabilities are then used to (a) guide the optimisation process toward solutions satisfying our stability criteria and (b) post-filter results to find the best stable solution. We exhibit our algorithm on synthetic and real-world problems and demonstrate that it is able to effectively find stable maxima.