Reinforcement learning algorithms have had tremendous successes in online learning settings. However, these successes have relied on low-stakes interactions between the algorithmic agent and its environment. In many settings where RL could be of use, such as health care and autonomous driving, the mistakes made by most online RL algorithms during early training come with unacceptable costs. These settings require developing reinforcement learning algorithms that can operate in the so-called batch setting, where the algorithms must learn from set of data that is fixed, finite, and generated from some (possibly unknown) policy. Evaluating policies different from the one that collected the data is called off-policy evaluation, and naturally poses counter-factual questions. In this project we show how off-policy evaluation and the estimation of treatment effects in causal inference are two approaches to the same problem, and compare recent progress in these two areas.

Most existing black-box optimization methods assume that all variables in the system being optimized have equal cost and can change freely at each iteration. However, in many real world systems, inputs are passed through a sequence of different operations or modules, making variables in earlier stages of processing more costly to update. Such structure imposes a cost on switching variables in early parts of a data processing pipeline. In this work, we propose a new algorithm for switch cost-aware optimization called Lazy Modular Bayesian Optimization (LaMBO). This method efficiently identifies the global optimum while minimizing cost through a passive change of variables in early modules. The method is theoretical grounded and achieves vanishing regret when augmented with switching cost. We apply LaMBO to multiple synthetic functions and a three-stage image segmentation pipeline used in a neuroscience application, where we obtain promising improvements over prevailing cost-aware Bayesian optimization algorithms. Our results demonstrate that LaMBO is an effective strategy for black-box optimization that is capable of minimizing switching costs in modular systems.

Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes two major contributions, we first find an unbiased estimator for the log-likelihood estimator of the Hawkes process to enable efficient use of the stochastic gradient descent method for maximum likelihood estimation. The second contribution is, we propose a specific single hidden layered neural network for the non-parametric estimation of the underlying kernels of the MHP. We evaluate the proposed model on both synthetic and real datasets, and find the method has comparable or better performance than existing estimation methods. The use of shallow neural network ensures that we do not compromise on the interpretability of the Hawkes model, while at the same time have the flexibility to estimate any non-standard Hawkes excitation kernel.

Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical models and show that they reduce to Bayesian networks with a pre-defined topology and a learnable density at each node. From this new perspective, we provide three results. First, we show that stacking multiple transformations in a normalizing flow relaxes independence assumptions and entangles the model distribution. Second, we show that a fundamental leap of capacity emerges when the depth of affine flows exceeds 3 transformation layers. Third, we prove the non-universality of the affine normalizing flow, regardless of its depth.

We propose a principled kernel-based policy iteration algorithm to solve the continuous-state Markov Decision Processes (MDPs). In contrast to most decision-theoretic planning frameworks, which assume fully known state transition models, we design a method that eliminates such a strong assumption, which is oftentimes extremely difficult to engineer in reality. To achieve this, we first apply the second-order Taylor expansion of the value function. The Bellman optimality equation is then approximated by a partial differential equation, which only relies on the first and second moments of the transition model. By combining the kernel representation of value function, we then design an efficient policy iteration algorithm whose policy evaluation step can be represented as a linear system of equations characterized by a finite set of supporting states. We have validated the proposed method through extensive simulations in both simplified and realistic planning scenarios, and the experiments show that our proposed approach leads to a much superior performance over several baseline methods.

To maximize cumulative user engagement (e.g. cumulative clicks) in sequential recommendation, it is often needed to tradeoff two potentially conflicting objectives, that is, pursuing higher immediate user engagement (e.g., click-through rate) and encouraging user browsing (i.e., more items exposured). Existing works often study these two tasks separately, thus tend to result in sub-optimal results. In this paper, we study this problem from an online optimization perspective, and propose a flexible and practical framework to explicitly tradeoff longer user browsing length and high immediate user engagement. Specifically, by considering items as actions, user's requests as states and user leaving as an absorbing state, we formulate each user's behavior as a personalized Markov decision process (MDP), and the problem of maximizing cumulative user engagement is reduced to a stochastic shortest path (SSP) problem. Meanwhile, with immediate user engagement and quit probability estimation, it is shown that the SSP problem can be efficiently solved via dynamic programming. Experiments on real-world datasets demonstrate the effectiveness of the proposed approach. Moreover, this approach is deployed at a large E-commerce platform, achieved over 7% improvement of cumulative clicks.

Learning interpretable and disentangled representations of data is a key topic in machine learning research. Variational Autoencoder (VAE) is a scalable method for learning directed latent variable models of complex data. It employs a clear and interpretable objective that can be easily optimized. However, this objective does not provide an explicit measure for the quality of latent variable representations which may result in their poor quality. We propose Variational Mutual Information Maximization Framework for VAE to address this issue. In comparison to other methods, it provides an explicit objective that maximizes lower bound on mutual information between latent codes and observations. The objective acts as a regularizer that forces VAE to not ignore the latent variable and allows one to select particular components of it to be most informative with respect to the observations. On top of that, the proposed framework provides a way to evaluate mutual information between latent codes and observations for a fixed VAE model. We have conducted our experiments on VAE models with Gaussian and joint Gaussian and discrete latent variables. Our results illustrate that the proposed approach strengthens relationships between latent codes and observations and improves learned representations.

Estimation of patient-specific model parameters is important for personalized modeling, although sparse and noisy clinical data can introduce significant uncertainty in the estimated parameter values. This importance source of uncertainty, if left unquantified, will lead to unknown variability in model outputs that hinder their reliable adoptions. Probabilistic estimation model parameters, however, remains an unresolved challenge because standard Markov Chain Monte Carlo sampling requires repeated model simulations that are computationally infeasible. A common solution is to replace the simulation model with a computationally-efficient surrogate for a faster sampling. However, by sampling from an approximation of the exact posterior probability density function (pdf) of the parameters, the efficiency is gained at the expense of sampling accuracy. In this paper, we address this issue by integrating surrogate modeling into Metropolis Hasting (MH) sampling of the exact posterior pdfs to improve its acceptance rate. It is done by first quickly constructing a Gaussian process (GP) surrogate of the exact posterior pdfs using deterministic optimization. This efficient surrogate is then used to modify commonly-used proposal distributions in MH sampling such that only proposals accepted by the surrogate will be tested by the exact posterior pdf for acceptance/rejection, reducing unnecessary model simulations at unlikely candidates. Synthetic and real-data experiments using the presented method show a significant gain in computational efficiency without compromising the accuracy. In addition, insights into the non-identifiability and heterogeneity of tissue properties can be gained from the obtained posterior distributions.

The data-centric construction of inexpensive surrogates for fine-grained, physical models has been at the forefront of computational physics due to its significant utility in many-query tasks such as uncertainty quantification. Recent efforts have taken advantage of the enabling technologies from the field of machine learning (e.g. deep neural networks) in combination with simulation data. While such strategies have shown promise even in higher-dimensional problems, they generally require large amounts of training data even though the construction of surrogates is by definition a Small Data problem. Rather than employing data-based loss functions, it has been proposed to make use of the governing equations (in the simplest case at collocation points) in order to imbue domain knowledge in the training of the otherwise black-box-like interpolators. The present paper provides a flexible, probabilistic framework that accounts for physical structure and information both in the training objectives as well as in the surrogate model itself. We advocate a probabilistic (Bayesian) model in which equalities that are available from the physics (e.g. residuals, conservation laws) can be introduced as virtual observables and can provide additional information through the likelihood. We further advocate a generative model i.e. one that attempts to learn the joint density of inputs and outputs that is capable of making use of unlabeled data (i.e. only inputs) in a semi-supervised fashion in order to promote the discovery of lower-dimensional embeddings which are nevertheless predictive of the fine-grained model's output.

Gathering labeled data to train well-performing machine learning models is one of the critical challenges in many applications. Active learning aims at reducing the labeling costs by an efficient and effective allocation of costly labeling resources. In this article, we propose a decision-theoretic selection strategy that (1) directly optimizes the gain in misclassification error, and (2) uses a Bayesian approach by introducing a conjugate prior distribution to determine the class posterior to deal with uncertainties. By reformulating existing selection strategies within our proposed model, we can explain which aspects are not covered in current state-of-the-art and why this leads to the superior performance of our approach. Extensive experiments on a large variety of datasets and different kernels validate our claims.