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In this work, we propose a stochastic gradient descent (SGD) framework to design data-driven policy gradient descent algorithms for the linear quadratic regulator problem. Two alternative schemes are considered to estimate the policy…

We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm (RAGD), and show that for geodesically smooth and strongly convex problems, within a neighborhood of the minimizer whose radius depends on the condition number as…

Ridge regression is a popular method for dense least squares regularization. In this work, ridge regression is studied in the context of VAR model estimation and inference. The implications of anisotropic penalization are discussed and a…

This paper presents a robust reinforcement learning algorithm called robust deterministic policy gradient (RDPG), which reformulates the H-infinity control problem as a two-player zero-sum dynamic game between a user and an adversary. The…

Automated red teaming can discover rare model failures and generate challenging examples that can be used for training or evaluation. However, a core challenge in automated red teaming is ensuring that the attacks are both diverse and…

We introduce a generalized numerical algorithm to construct the solution landscape, which is a pathway map consisting of all stationary points and their connections. Based on the high-index optimization-based shrinking dimer (HiOSD) method…

Gradient-based methods for two-player games produce rich dynamics that can solve challenging problems, yet can be difficult to stabilize and understand. Part of this complexity originates from the discrete update steps given by simultaneous…

Risk-sensitive reinforcement learning (RL) is crucial for maintaining reliable performance in high-stakes applications. While traditional RL methods aim to learn a point estimate of the random cumulative cost, distributional RL (DRL) seeks…

A novel decentralised trajectory generation algorithm for Multi Agent systems is presented. Multi-robot systems have the capacity to transform lives in a variety of fields. But, trajectory generation for multi-robot systems is still in its…

In this work, we propose a simple kernel ridge regression (KRR) framework with a dynamic-aware validation strategy for long-term prediction of complex dynamical systems. By employing a data-driven kernel derived from diffusion maps, the…

We propose a new class of deep reinforcement learning (RL) algorithms that model latent representations in hyperbolic space. Sequential decision-making requires reasoning about the possible future consequences of current behavior.…

Inverse reinforcement learning (IRL) is the problem of finding a reward function that generates a given optimal policy for a given Markov Decision Process. This paper looks at an algorithmic-independent geometric analysis of the IRL problem…

Our goal is to improve variance reducing stochastic methods through better control variates. We first propose a modification of SVRG which uses the Hessian to track gradients over time, rather than to recondition, increasing the correlation…

The Vehicle Routing Problem (VRP) is a complex optimization problem with numerous real-world applications, mostly solved using metaheuristic algorithms due to its $\mathcal{NP}$-Hard nature. Traditionally, these metaheuristics rely on…

Robust Reinforcement Learning (RRL) is a promising Reinforcement Learning (RL) paradigm aimed at training robust to uncertainty or disturbances models, making them more efficient for real-world applications. Following this paradigm,…

A new variant of the GMRES method is presented for solving linear systems with the same matrix and subsequently obtained multiple right-hand sides. The new method keeps such properties of the classical GMRES algorithm as follows. Both bases…

Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…

Policy gradient (PG) methods are a widely used reinforcement learning methodology in many applications such as video games, autonomous driving, and robotics. In spite of its empirical success, a rigorous understanding of the global…

Goal-conditioned reinforcement learning (GCRL), related to a set of complex RL problems, trains an agent to achieve different goals under particular scenarios. Compared to the standard RL solutions that learn a policy solely depending on…

In recent years, reinforcement learning (RL) systems with general goals beyond a cumulative sum of rewards have gained traction, such as in constrained problems, exploration, and acting upon prior experiences. In this paper, we consider…