We propose an end-to-end trainable framework that processes large-scale visual data tensors by looking \emph{at a fraction of their entries only}. Our method combines a neural network encoder with a \emph{tensor train decomposition} to learn a low-rank latent encoding, coupled with cross-approximation (CA) to learn the representation through a subset of the original samples. CA is an adaptive sampling algorithm that is native to tensor decompositions and avoids working with the full high-resolution data explicitly. Instead, it actively selects local representative samples that we fetch out-of-core and on-demand. The required number of samples grows only logarithmically with the size of the input. Our implicit representation of the tensor in the network enables processing large grids that could not be otherwise tractable in their uncompressed form. The proposed approach is particularly useful for large-scale multidimensional grid data (e.g., 3D tomography), and for tasks that require context over a large receptive field (e.g., predicting the medical condition of entire organs). The code will be available at https://github.com/aelphy/c-pic
Causal structure learning is a key problem in many domains. Causal structures can be learnt by performing experiments on the system of interest. We address the largely unexplored problem of designing experiments that simultaneously intervene on multiple variables. While potentially more informative than the commonly considered single-variable interventions, selecting such interventions is algorithmically much more challenging, due to the doubly-exponential combinatorial search space over sets of composite interventions. In this paper, we develop efficient algorithms for optimizing different objective functions quantifying the informativeness of experiments. By establishing novel submodularity properties of these objectives, we provide approximation guarantees for our algorithms. Our algorithms empirically perform superior to both random interventions and algorithms that only select single-variable interventions.
Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems. In this work, we propose a general, fully differentiable framework for Bayesian structure learning (DiBS) that operates in the continuous space of a latent probabilistic graph representation. Building on recent advances in variational inference, we use DiBS to devise an efficient method for approximating posteriors over structural models. Contrary to existing work, DiBS is agnostic to the form of the local conditional distributions and allows for joint posterior inference of both the graph structure and the conditional distribution parameters. This makes our method directly applicable to posterior inference of nonstandard Bayesian network models, e.g., with nonlinear dependencies encoded by neural networks. In evaluations on simulated and real-world data, DiBS significantly outperforms related approaches to joint posterior inference.
We consider Bayesian optimization in settings where observations can be adversarially biased, for example by an uncontrolled hidden confounder. Our first contribution is a reduction of the confounded setting to the dueling bandit model. Then we propose a novel approach for dueling bandits based on information-directed sampling (IDS). Thereby, we obtain the first efficient kernelized algorithm for dueling bandits that comes with cumulative regret guarantees. Our analysis further generalizes a previously proposed semi-parametric linear bandit model to non-linear reward functions, and uncovers interesting links to doubly-robust estimation.
The goal of this paper is to characterize Gaussian-Process optimization in the setting where the function domain is large relative to the number of admissible function evaluations, i.e., where it is impossible to find the global optimum. We provide upper bounds on the suboptimality (Bayesian simple regret) of the solution found by optimization strategies that are closely related to the widely used expected improvement (EI) and upper confidence bound (UCB) algorithms. These regret bounds illuminate the relationship between the number of evaluations, the domain size (i.e. cardinality of finite domains / Lipschitz constant of the covariance function in continuous domains), and the optimality of the retrieved function value. In particular, they show that even when the number of evaluations is far too small to find the global optimum, we can find nontrivial function values (e.g. values that achieve a certain ratio with the optimal value).
Bayesian Optimization (BO) is a successful methodology to tune the hyperparameters of machine learning algorithms. The user defines a metric of interest, such as the validation error, and BO finds the optimal hyperparameters that minimize it. However, the metric improvements on the validation set may not translate to the test set, especially on small datasets. In other words, BO can overfit. While cross-validation mitigates this, it comes with high computational cost. In this paper, we carry out the first systematic investigation of overfitting in BO and demonstrate that this is a serious yet often overlooked concern in practice. We propose the first problem-adaptive and interpretable criterion to early stop BO, reducing overfitting while mitigating the cost of cross-validation. Experimental results on real-world hyperparameter optimization tasks show that our approach can substantially reduce compute time with little to no loss of test accuracy,demonstrating a clear practical advantage over existing techniques.
In real-world tasks, reinforcement learning (RL) agents frequently encounter situations that are not present during training time. To ensure reliable performance, the RL agents need to exhibit robustness against worst-case situations. The robust RL framework addresses this challenge via a worst-case optimization between an agent and an adversary. Previous robust RL algorithms are either sample inefficient, lack robustness guarantees, or do not scale to large problems. We propose the Robust Hallucinated Upper-Confidence RL (RH-UCRL) algorithm to provably solve this problem while attaining near-optimal sample complexity guarantees. RH-UCRL is a model-based reinforcement learning (MBRL) algorithm that effectively distinguishes between epistemic and aleatoric uncertainty and efficiently explores both the agent and adversary decision spaces during policy learning. We scale RH-UCRL to complex tasks via neural networks ensemble models as well as neural network policies. Experimentally, we demonstrate that RH-UCRL outperforms other robust deep RL algorithms in a variety of adversarial environments.
For many reinforcement learning (RL) applications, specifying a reward is difficult. In this paper, we consider an RL setting where the agent can obtain information about the reward only by querying an expert that can, for example, evaluate individual states or provide binary preferences over trajectories. From such expensive feedback, we aim to learn a model of the reward function that allows standard RL algorithms to achieve high expected return with as few expert queries as possible. For this purpose, we propose Information Directed Reward Learning (IDRL), which uses a Bayesian model of the reward function and selects queries that maximize the information gain about the difference in return between potentially optimal policies. In contrast to prior active reward learning methods designed for specific types of queries, IDRL naturally accommodates different query types. Moreover, by shifting the focus from reducing the reward approximation error to improving the policy induced by the reward model, it achieves similar or better performance with significantly fewer queries. We support our findings with extensive evaluations in multiple environments and with different types of queries.
Training Reinforcement Learning (RL) agents in high-stakes applications might be too prohibitive due to the risk associated to exploration. Thus, the agent can only use data previously collected by safe policies. While previous work considers optimizing the average performance using offline data, we focus on optimizing a risk-averse criteria, namely the CVaR. In particular, we present the Offline Risk-Averse Actor-Critic (O-RAAC), a model-free RL algorithm that is able to learn risk-averse policies in a fully offline setting. We show that O-RAAC learns policies with higher CVaR than risk-neutral approaches in different robot control tasks. Furthermore, considering risk-averse criteria guarantees distributional robustness of the average performance with respect to particular distribution shifts. We demonstrate empirically that in the presence of natural distribution-shifts, O-RAAC learns policies with good average performance.
Combinatorial bandits with semi-bandit feedback generalize multi-armed bandits, where the agent chooses sets of arms and observes a noisy reward for each arm contained in the chosen set. The action set satisfies a given structure such as forming a base of a matroid or a path in a graph. We focus on the pure-exploration problem of identifying the best arm with fixed confidence, as well as a more general setting, where the structure of the answer set differs from the one of the action set. Using the recently popularized game framework, we interpret this problem as a sequential zero-sum game and develop a CombGame meta-algorithm whose instances are asymptotically optimal algorithms with finite time guarantees. In addition to comparing two families of learners to instantiate our meta-algorithm, the main contribution of our work is a specific oracle efficient instance for best-arm identification with combinatorial actions. Based on a projection-free online learning algorithm for convex polytopes, it is the first computationally efficient algorithm which is asymptotically optimal and has competitive empirical performance.