Regularized Robust MDPs and Risk-Sensitive MDPs: Equivalence, Policy Gradient, and Sample Complexity

This paper focuses on reinforcement learning for the regularized robust Markov decision process (MDP) problem, an extension of the robust MDP framework. We first introduce the risk-sensitive MDP and establish the equivalence between risk-sensitive MDP and regularized robust MDP. This equivalence offers an alternative perspective for addressing the regularized RMDP and enables the design of efficient learning algorithms. Given this equivalence, we further derive the policy gradient theorem for the regularized robust MDP problem and prove the global convergence of the exact policy gradient method under the tabular setting with direct parameterization. We also propose a sample-based offline learning algorithm, namely the robust fitted-Z iteration (RFZI), for a specific regularized robust MDP problem with a KL-divergence regularization term and analyze the sample complexity of the algorithm. Our results are also supported by numerical simulations.

Non-asymptotic System Identification for Linear Systems with Nonlinear Policies

This paper considers a single-trajectory system identification problem for linear systems under general nonlinear and/or time-varying policies with i.i.d. random excitation noises. The problem is motivated by safe learning-based control for constrained linear systems, where the safe policies during the learning process are usually nonlinear and time-varying for satisfying the state and input constraints. In this paper, we provide a non-asymptotic error bound for least square estimation when the data trajectory is generated by any nonlinear and/or time-varying policies as long as the generated state and action trajectories are bounded. This significantly generalizes the existing non-asymptotic guarantees for linear system identification, which usually consider i.i.d. random inputs or linear policies. Interestingly, our error bound is consistent with that for linear policies with respect to the dependence on the trajectory length, system dimensions, and excitation levels. Lastly, we demonstrate the applications of our results by safe learning with robust model predictive control and provide numerical analysis.

Ultra-Fine Entity Typing with Prior Knowledge about Labels: A Simple Clustering Based Strategy

Ultra-fine entity typing (UFET) is the task of inferring the semantic types, from a large set of fine-grained candidates, that apply to a given entity mention. This task is especially challenging because we only have a small number of training examples for many of the types, even with distant supervision strategies. State-of-the-art models, therefore, have to rely on prior knowledge about the type labels in some way. In this paper, we show that the performance of existing methods can be improved using a simple technique: we use pre-trained label embeddings to cluster the labels into semantic domains and then treat these domains as additional types. We show that this strategy consistently leads to improved results, as long as high-quality label embeddings are used. We furthermore use the label clusters as part of a simple post-processing technique, which results in further performance gains. Both strategies treat the UFET model as a black box and can thus straightforwardly be used to improve a wide range of existing models.

Distilling Semantic Concept Embeddings from Contrastively Fine-Tuned Language Models

Learning vectors that capture the meaning of concepts remains a fundamental challenge. Somewhat surprisingly, perhaps, pre-trained language models have thus far only enabled modest improvements to the quality of such concept embeddings. Current strategies for using language models typically represent a concept by averaging the contextualised representations of its mentions in some corpus. This is potentially sub-optimal for at least two reasons. First, contextualised word vectors have an unusual geometry, which hampers downstream tasks. Second, concept embeddings should capture the semantic properties of concepts, whereas contextualised word vectors are also affected by other factors. To address these issues, we propose two contrastive learning strategies, based on the view that whenever two sentences reveal similar properties, the corresponding contextualised vectors should also be similar. One strategy is fully unsupervised, estimating the properties which are expressed in a sentence from the neighbourhood structure of the contextualised word embeddings. The second strategy instead relies on a distant supervision signal from ConceptNet. Our experimental results show that the resulting vectors substantially outperform existing concept embeddings in predicting the semantic properties of concepts, with the ConceptNet-based strategy achieving the best results. These findings are furthermore confirmed in a clustering task and in the downstream task of ontology completion.

Stochastic Nonlinear Control via Finite-dimensional Spectral Dynamic Embedding

Optimal control is notoriously difficult for stochastic nonlinear systems. Ren et al. introduced Spectral Dynamics Embedding for developing reinforcement learning methods for controlling an unknown system. It uses an infinite-dimensional feature to linearly represent the state-value function and exploits finite-dimensional truncation approximation for practical implementation. However, the finite-dimensional approximation properties in control have not been investigated even when the model is known. In this paper, we provide a tractable stochastic nonlinear control algorithm that exploits the nonlinear dynamics upon the finite-dimensional feature approximation, Spectral Dynamics Embedding Control (SDEC), with an in-depth theoretical analysis to characterize the approximation error induced by the finite-dimension truncation and statistical error induced by finite-sample approximation in both policy evaluation and policy optimization. We also empirically test the algorithm and compare the performance with Koopman-based methods and iLQR methods on the pendulum swingup problem.

Decentralized Riemannian natural gradient methods with Kronecker-product approximations

With a computationally efficient approximation of the second-order information, natural gradient methods have been successful in solving large-scale structured optimization problems. We study the natural gradient methods for the large-scale decentralized optimization problems on Riemannian manifolds, where the local objective function defined by the local dataset is of a log-probability type. By utilizing the structure of the Riemannian Fisher information matrix (RFIM), we present an efficient decentralized Riemannian natural gradient descent (DRNGD) method. To overcome the communication issue of the high-dimension RFIM, we consider a class of structured problems for which the RFIM can be approximated by a Kronecker product of two low-dimension matrices. By performing the communications over the Kronecker factors, a high-quality approximation of the RFIM can be obtained in a low cost. We prove that DRNGD converges to a stationary point with the best-known rate of $\mathcal{O}(1/K)$. Numerical experiments demonstrate the efficiency of our proposed method compared with the state-of-the-art ones. To the best of our knowledge, this is the first Riemannian second-order method for solving decentralized manifold optimization problems.

Gaussian Max-Value Entropy Search for Multi-Agent Bayesian Optimization

We study the multi-agent Bayesian optimization (BO) problem, where multiple agents maximize a black-box function via iterative queries. We focus on Entropy Search (ES), a sample-efficient BO algorithm that selects queries to maximize the mutual information about the maximum of the black-box function. One of the main challenges of ES is that calculating the mutual information requires computationally-costly approximation techniques. For multi-agent BO problems, the computational cost of ES is exponential in the number of agents. To address this challenge, we propose the Gaussian Max-value Entropy Search, a multi-agent BO algorithm with favorable sample and computational efficiency. The key to our idea is to use a normal distribution to approximate the function maximum and calculate its mutual information accordingly. The resulting approximation allows queries to be cast as the solution of a closed-form optimization problem which, in turn, can be solved via a modified gradient ascent algorithm and scaled to a large number of agents. We demonstrate the effectiveness of Gaussian max-value Entropy Search through numerical experiments on standard test functions and real-robot experiments on the source-seeking problem. Results show that the proposed algorithm outperforms the multi-agent BO baselines in the numerical experiments and can stably seek the source with a limited number of noisy observations on real robots.

Latent Variable Representation for Reinforcement Learning

Deep latent variable models have achieved significant empirical successes in model-based reinforcement learning (RL) due to their expressiveness in modeling complex transition dynamics. On the other hand, it remains unclear theoretically and empirically how latent variable models may facilitate learning, planning, and exploration to improve the sample efficiency of RL. In this paper, we provide a representation view of the latent variable models for state-action value functions, which allows both tractable variational learning algorithm and effective implementation of the optimism/pessimism principle in the face of uncertainty for exploration. In particular, we propose a computationally efficient planning algorithm with UCB exploration by incorporating kernel embeddings of latent variable models. Theoretically, we establish the sample complexity of the proposed approach in the online and offline settings. Empirically, we demonstrate superior performance over current state-of-the-art algorithms across various benchmarks.

Learning to Optimize with Stochastic Dominance Constraints

In real-world decision-making, uncertainty is important yet difficult to handle. Stochastic dominance provides a theoretically sound approach for comparing uncertain quantities, but optimization with stochastic dominance constraints is often computationally expensive, which limits practical applicability. In this paper, we develop a simple yet efficient approach for the problem, the Light Stochastic Dominance Solver (light-SD), that leverages useful properties of the Lagrangian. We recast the inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses apparent intractability and leads to tractable updates or even closed-form solutions for gradient calculations. We prove convergence of the algorithm and test it empirically. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.