Ayman Boustati

Ayman Boustati, Hana Chockler, Daniel C. McNamee

The ability to adapt to changes in environmental contingencies is an important challenge in reinforcement learning. Indeed, transferring previously acquired knowledge to environments with unseen structural properties can greatly enhance the flexibility and efficiency by which novel optimal policies may be constructed. In this work, we study the problem of transfer learning under changes in the environment dynamics. In this study, we apply causal reasoning in the offline reinforcement learning setting to transfer a learned policy to new environments. Specifically, we use the Decision Transformer (DT) architecture to distill a new policy on the new environment. The DT is trained on data collected by performing policy rollouts on factual and counterfactual simulations from the source environment. We show that this mechanism can bootstrap a successful policy on the target environment while retaining most of the reward.

Lorenz Richter, Ayman Boustati, Nikolas Nüsken et al.

We analyse the properties of an unbiased gradient estimator of the ELBO for variational inference, based on the score function method with leave-one-out control variates. We show that this gradient estimator can be obtained using a new loss, defined as the variance of the log-ratio between the exact posterior and the variational approximation, which we call the $\textit{log-variance loss}$. Under certain conditions, the gradient of the log-variance loss equals the gradient of the (negative) ELBO. We show theoretically that this gradient estimator, which we call $\textit{VarGrad}$ due to its connection to the log-variance loss, exhibits lower variance than the score function method in certain settings, and that the leave-one-out control variate coefficients are close to the optimal ones. We empirically demonstrate that VarGrad offers a favourable variance versus computation trade-off compared to other state-of-the-art estimators on a discrete VAE.

Ayman Boustati, Sattar Vakili, James Hensman et al.

Approximate inference in complex probabilistic models such as deep Gaussian processes requires the optimisation of doubly stochastic objective functions. These objectives incorporate randomness both from mini-batch subsampling of the data and from Monte Carlo estimation of expectations. If the gradient variance is high, the stochastic optimisation problem becomes difficult with a slow rate of convergence. Control variates can be used to reduce the variance, but past approaches do not take into account how mini-batch stochasticity affects sampling stochasticity, resulting in sub-optimal variance reduction. We propose a new approach in which we use a recognition network to cheaply approximate the optimal control variate for each mini-batch, with no additional model gradient computations. We illustrate the properties of this proposal and test its performance on logistic regression and deep Gaussian processes.

Ayman Boustati, Ömer Deniz Akyildiz, Theodoros Damoulas et al.

We introduce a framework for inference in general state-space hidden Markov models (HMMs) under likelihood misspecification. In particular, we leverage the loss-theoretic perspective of Generalized Bayesian Inference (GBI) to define generalised filtering recursions in HMMs, that can tackle the problem of inference under model misspecification. In doing so, we arrive at principled procedures for robust inference against observation contamination by utilising the $β$-divergence. Operationalising the proposed framework is made possible via sequential Monte Carlo methods (SMC), where most standard particle methods, and their associated convergence results, are readily adapted to the new setting. We apply our approach to object tracking and Gaussian process regression problems, and observe improved performance over both standard filtering algorithms and other robust filters.

Ayman Boustati, Theodoros Damoulas, Richard S. Savage

We present a multi-task learning formulation for Deep Gaussian processes (DGPs), through non-linear mixtures of latent processes. The latent space is composed of private processes that capture within-task information and shared processes that capture across-task dependencies. We propose two different methods for segmenting the latent space: through hard coding shared and task-specific processes or through soft sharing with Automatic Relevance Determination kernels. We show that our formulation is able to improve the learning performance and transfer information between the tasks, outperforming other probabilistic multi-task learning models across real-world and benchmarking settings.