Policy gradient methods have become a standard for training reinforcement learning agents in a scalable and efficient manner. However, they do not account for transition uncertainty, whereas learning robust policies can be computationally expensive. In this paper, we introduce robust policy gradient (RPG), a policy-based method that efficiently solves rectangular robust Markov decision processes (MDPs). We provide a closed-form expression for the worst occupation measure. Incidentally, we find that the worst kernel is a rank-one perturbation of the nominal. Combining the worst occupation measure with a robust Q-value estimation yields an explicit form of the robust gradient. Our resulting RPG can be estimated from data with the same time complexity as its non-robust equivalent. Hence, it relieves the computational burden of convex optimization problems required for training robust policies by current policy gradient approaches.

In robust Markov decision processes (RMDPs), it is assumed that the reward and the transition dynamics lie in a given uncertainty set. By targeting maximal return under the most adversarial model from that set, RMDPs address performance sensitivity to misspecified environments. Yet, to preserve computational tractability, the uncertainty set is traditionally independently structured for each state. This so-called rectangularity condition is solely motivated by computational concerns. As a result, it lacks a practical incentive and may lead to overly conservative behavior. In this work, we study coupled reward RMDPs where the transition kernel is fixed, but the reward function lies within an $\alpha$-radius from a nominal one. We draw a direct connection between this type of non-rectangular reward-RMDPs and applying policy visitation frequency regularization. We introduce a policy-gradient method, and prove its convergence. Numerical experiments illustrate the learned policy's robustness and its less conservative behavior when compared to rectangular uncertainty.

In Reinforcement Learning (RL), the goal of agents is to discover an optimal policy that maximizes the expected cumulative rewards. This objective may also be viewed as finding a policy that optimizes a linear function of its state-action occupancy measure, hereafter referred as Linear RL. However, many supervised and unsupervised RL problems are not covered in the Linear RL framework, such as apprenticeship learning, pure exploration and variational intrinsic control, where the objectives are non-linear functions of the occupancy measures. RL with non-linear utilities looks unwieldy, as methods like Bellman equation, value iteration, policy gradient, dynamic programming that had tremendous success in Linear RL, fail to trivially generalize. In this paper, we derive the policy gradient theorem for RL with general utilities. The policy gradient theorem proves to be a cornerstone in Linear RL due to its elegance and ease of implementability. Our policy gradient theorem for RL with general utilities shares the same elegance and ease of implementability. Based on the policy gradient theorem derived, we also present a simple sample-based algorithm. We believe our results will be of interest to the community and offer inspiration to future works in this generalized setting.

In reinforcement learning (RL), we are concerned with learning good policies for sequential decisionmaking problems modeled as Markov Decision Processes (MDPs) [29, 35]. MDPs assume that the transition model of the environment is fixed across training and testing, but this is often violated in practical applications. For example, when deploying a simulator-trained robot in reality, a notable challenge is the substantial disparity between the simulated environment and the intricate complexities of the real world, leading to potential subpar performance upon deployment. Such a mismatch may significantly degrade the performance of the trained policy in testing. To deal with this issue, the robust MDP (RMDP) framework has been introduced in [16, 24, 44], aiming to learn policies that are robust to perturbation of the transition model within an uncertainty set.

In Markov Decision Processes (MDPs), an agent interacts with the environment and learns to optimally behave in it [28]. However, the MDP solution may be very sensitive to little changes in the model parameters [23]. Hence we should be cautious applying the solution of the MDP, when the model is changing or when there is uncertainty in the model parameters. Robust MDPs provide a way to address this issue, where an agent can learn to optimally behave even when the model parameters are uncertain [15, 29, 18]. Another motivation to study robust MDPs is that they can lead to better generalization [33, 34, 25] compared to non-robust solutions.

We present an approach towards convex optimization that relies on a novel scheme which converts adaptive online algorithms into offline methods. In the offline optimization setting, our derived methods are shown to obtain favourable adaptive guarantees which depend on the harmonic sum of the queried gradients. We further show that our methods implicitly adapt to the objective's structure: in the smooth case fast convergence rates are ensured without any prior knowledge of the smoothness parameter, while still maintaining guarantees in the non-smooth setting. Our approach has a natural extension to the stochastic setting, resulting in a lazy version of SGD (stochastic GD), where minibathces are chosen adaptively depending on the magnitude of the gradients.

DR-submodular continuous functions are important objectives with wide real-world applications spanning MAP inference in determinantal point processes (DPPs), and mean-field inference for probabilistic submodular models, amongst others. DR-submodularity captures a subclass of non-convex functions that enables both exact minimization and approximate maximization in polynomial time. In this work we study the problem of maximizing non-monotone DR-submodular continuous functions under general down-closed convex constraints. We start by investigating geometric properties that underlie such objectives, e.g., a strong relation between (approximately) stationary points and global optimum is proved. These properties are then used to devise two optimization algorithms with provable guarantees. Concretely, we first devise a "two-phase'' algorithm with 1/4 approximation guarantee. This algorithm allows the use of existing methods for finding (approximately) stationary points as a subroutine, thus, harnessing recent progress in non-convex optimization. Then we present a non-monotone Frank-Wolfe variant with 1/e approximation guarantee and sublinear convergence rate. Finally, we extend our approach to a broader class of generalized DR-submodular continuous functions, which captures a wider spectrum of applications. Our theoretical findings are validated on synthetic and real-world problem instances.

The weighted k-nearest neighbors algorithm is one of the most fundamental non-parametric methods in pattern recognition and machine learning. The question of setting the optimal number of neighbors as well as the optimal weights has received much attention throughout the years, nevertheless this problem seems to have remained unsettled. In this paper we offer a simple approach to locally weighted regression/classification, where we make the bias-variance tradeoff explicit. Our formulation enables us to phrase a notion of optimal weights, and to efficiently find these weights as well as the optimal number of neighbors efficiently and adaptively, for each data point whose value we wish to estimate. The applicability of our approach is demonstrated on several datasets, showing superior performance over standard locally weighted methods.

This poster has been moved from Monday #86 to Thursday #101. Stochastic convex optimization is a basic and well studied primitive in machine learning. It is well known that convex and Lipschitz functions can be minimized efficiently using Stochastic Gradient Descent (SGD).The Normalized Gradient Descent (NGD) algorithm, is an adaptation of Gradient Descent, which updates according to the direction of the gradients, rather than the gradients themselves. In this paper we analyze a stochastic version of NGD and prove its convergence to a global minimum for a wider class of functions: we require the functions to be quasi-convex and locally-Lipschitz. Quasi-convexity broadens the concept of unimodality to multidimensions and allows for certain types of saddle points, which are a known hurdle for first-order optimization methods such as gradient descent. Locally-Lipschitz functions are only required to be Lipschitz in a small region around the optimum. This assumption circumvents gradient explosion, which is another known hurdle for gradient descent variants. Interestingly, unlike the vanilla SGD algorithm, the stochastic normalized gradient descent algorithm provably requires a minimal minibatch size.

We consider Empirical Risk Minimization (ERM) in the context of stochastic optimization with exp-concave and smooth losses---a general optimization framework that captures several important learning problems including linear and logistic regression, learning SVMs with the squared hinge-loss, portfolio selection and more. In this setting, we establish the first evidence that ERM is able to attain fast generalization rates, and show that the expected loss of the ERM solution in $d$ dimensions converges to the optimal expected loss in a rate of $d/n$. This rate matches existing lower bounds up to constants and improves by a $\log{n}$ factor upon the state-of-the-art, which is only known to be attained by an online-to-batch conversion of computationally expensive online algorithms.