Offline policy learning (OPL) leverages existing data collected a priori for policy optimization without any active exploration. Despite the prevalence and recent interest in this problem, its theoretical and algorithmic foundations in function approximation settings remain under-developed. In this paper, we consider this problem on the axes of distributional shift, optimization, and generalization in offline contextual bandits with neural networks. In particular, we propose a provably efficient offline contextual bandit with neural network function approximation that does not require any functional assumption on the reward. We show that our method provably generalizes over unseen contexts under a milder condition for distributional shift than the existing OPL works. Notably, unlike any other OPL method, our method learns from the offline data in an online manner using stochastic gradient descent, allowing us to leverage the benefits of online learning into an offline setting. Moreover, we show that our method is more computationally efficient and has a better dependence on the effective dimension of the neural network than an online counterpart. Finally, we demonstrate the empirical effectiveness of our method in a range of synthetic and real-world OPL problems.
相關內容
In black-box function optimization, we need to consider not only controllable design variables but also uncontrollable stochastic environment variables. In such cases, it is necessary to solve the optimization problem by taking into account the uncertainty of the environmental variables. Chance-constrained (CC) problem, the problem of maximizing the expected value under a certain level of constraint satisfaction probability, is one of the practically important problems in the presence of environmental variables. In this study, we consider distributionally robust CC (DRCC) problem and propose a novel DRCC Bayesian optimization method for the case where the distribution of the environmental variables cannot be precisely specified. We show that the proposed method can find an arbitrary accurate solution with high probability in a finite number of trials, and confirm the usefulness of the proposed method through numerical experiments.
A key challenge facing deep learning is that neural networks are often not robust to shifts in the underlying data distribution. We study this problem from the perspective of the statistical concept of parameter identification. Generalization bounds from learning theory often assume that the test distribution is close to the training distribution. In contrast, if we can identify the "true" parameters, then the model generalizes to arbitrary distribution shifts. However, neural networks typically have internal symmetries that make parameter identification impossible. We show that we can identify the function represented by a quadratic network even though we cannot identify its parameters; we extend this result to neural networks with ReLU activations. Thus, we can obtain robust generalization bounds for neural networks. We leverage this result to obtain new bounds for contextual bandits and transfer learning with quadratic neural networks. Overall, our results suggest that we can improve robustness of neural networks by designing models that can represent the true data generating process.
Second-order optimizers are thought to hold the potential to speed up neural network training, but due to the enormous size of the curvature matrix, they typically require approximations to be computationally tractable. The most successful family of approximations are Kronecker-Factored, block-diagonal curvature estimates (KFAC). Here, we combine tools from prior work to evaluate exact second-order updates with careful ablations to establish a surprising result: Due to its approximations, KFAC is not closely related to second-order updates, and in particular, it significantly outperforms true second-order updates. This challenges widely held believes and immediately raises the question why KFAC performs so well. We answer this question by showing that KFAC approximates a first-order algorithm, which performs gradient descent on neurons rather than weights. Finally, we show that this optimizer often improves over KFAC in terms of computational cost and data-efficiency.
In today's technology environment, information is abundant, dynamic, and heterogeneous in nature. Automated filtering and prioritization of information is based on the distinction between whether the information adds substantial value toward one's goal or not. Contextual multi-armed bandit has been widely used for learning to filter contents and prioritize according to user interest or relevance. Learn-to-Rank technique optimizes the relevance ranking on items, allowing the contents to be selected accordingly. We propose a novel approach to top-K rankings under the contextual multi-armed bandit framework. We model the stochastic reward function with a neural network to allow non-linear approximation to learn the relationship between rewards and contexts. We demonstrate the approach and evaluate the the performance of learning from the experiments using real world data sets in simulated scenarios. Empirical results show that this approach performs well under the complexity of a reward structure and high dimensional contextual features.
Approximate Bayesian computation (ABC) is a popular likelihood-free inference method for models with intractable likelihood functions. As ABC methods usually rely on comparing summary statistics of observed and simulated data, the choice of the statistics is crucial. This choice involves a trade-off between loss of information and dimensionality reduction, and is often determined based on domain knowledge. However, handcrafting and selecting suitable statistics is a laborious task involving multiple trial-and-error steps. In this work, we introduce an active learning method for ABC statistics selection which reduces the domain expert's work considerably. By involving the experts, we are able to handle misspecified models, unlike the existing dimension reduction methods. Moreover, empirical results show better posterior estimates than with existing methods, when the simulation budget is limited.
Computational design problems arise in a number of settings, from synthetic biology to computer architectures. In this paper, we aim to solve data-driven model-based optimization (MBO) problems, where the goal is to find a design input that maximizes an unknown objective function provided access to only a static dataset of prior experiments. Such data-driven optimization procedures are the only practical methods in many real-world domains where active data collection is expensive (e.g., when optimizing over proteins) or dangerous (e.g., when optimizing over aircraft designs). Typical methods for MBO that optimize the design against a learned model suffer from distributional shift: it is easy to find a design that "fools" the model into predicting a high value. To overcome this, we propose conservative objective models (COMs), a method that learns a model of the objective function that lower bounds the actual value of the ground-truth objective on out-of-distribution inputs, and uses it for optimization. Structurally, COMs resemble adversarial training methods used to overcome adversarial examples. COMs are simple to implement and outperform a number of existing methods on a wide range of MBO problems, including optimizing protein sequences, robot morphologies, neural network weights, and superconducting materials.
The difficulty in specifying rewards for many real-world problems has led to an increased focus on learning rewards from human feedback, such as demonstrations. However, there are often many different reward functions that explain the human feedback, leaving agents with uncertainty over what the true reward function is. While most policy optimization approaches handle this uncertainty by optimizing for expected performance, many applications demand risk-averse behavior. We derive a novel policy gradient-style robust optimization approach, PG-BROIL, that optimizes a soft-robust objective that balances expected performance and risk. To the best of our knowledge, PG-BROIL is the first policy optimization algorithm robust to a distribution of reward hypotheses which can scale to continuous MDPs. Results suggest that PG-BROIL can produce a family of behaviors ranging from risk-neutral to risk-averse and outperforms state-of-the-art imitation learning algorithms when learning from ambiguous demonstrations by hedging against uncertainty, rather than seeking to uniquely identify the demonstrator's reward function.
A core capability of intelligent systems is the ability to quickly learn new tasks by drawing on prior experience. Gradient (or optimization) based meta-learning has recently emerged as an effective approach for few-shot learning. In this formulation, meta-parameters are learned in the outer loop, while task-specific models are learned in the inner-loop, by using only a small amount of data from the current task. A key challenge in scaling these approaches is the need to differentiate through the inner loop learning process, which can impose considerable computational and memory burdens. By drawing upon implicit differentiation, we develop the implicit MAML algorithm, which depends only on the solution to the inner level optimization and not the path taken by the inner loop optimizer. This effectively decouples the meta-gradient computation from the choice of inner loop optimizer. As a result, our approach is agnostic to the choice of inner loop optimizer and can gracefully handle many gradient steps without vanishing gradients or memory constraints. Theoretically, we prove that implicit MAML can compute accurate meta-gradients with a memory footprint that is, up to small constant factors, no more than that which is required to compute a single inner loop gradient and at no overall increase in the total computational cost. Experimentally, we show that these benefits of implicit MAML translate into empirical gains on few-shot image recognition benchmarks.
In this paper, from a theoretical perspective, we study how powerful graph neural networks (GNNs) can be for learning approximation algorithms for combinatorial problems. To this end, we first establish a new class of GNNs that can solve strictly a wider variety of problems than existing GNNs. Then, we bridge the gap between GNN theory and the theory of distributed local algorithms to theoretically demonstrate that the most powerful GNN can learn approximation algorithms for the minimum dominating set problem and the minimum vertex cover problem with some approximation ratios and that no GNN can perform better than with these ratios. This paper is the first to elucidate approximation ratios of GNNs for combinatorial problems. Furthermore, we prove that adding coloring or weak-coloring to each node feature improves these approximation ratios. This indicates that preprocessing and feature engineering theoretically strengthen model capabilities.
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.
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