MDP Geometry, Normalization and Value Free Solvers

Markov Decision Process (MDP) is a common mathematical model for sequential decision-making problems. In this paper, we present a new geometric interpretation of MDP, which is useful for analyzing the dynamics of main MDP algorithms. Based on this interpretation, we demonstrate that MDPs can be split into equivalence classes with indistinguishable algorithm dynamics. The related normalization procedure allows for the design of a new class of MDP-solving algorithms that find optimal policies without computing policy values.

On Value Iteration Convergence in Connected MDPs

This paper establishes that an MDP with a unique optimal policy and ergodic associated transition matrix ensures the convergence of various versions of the Value Iteration algorithm at a geometric rate that exceeds the discount factor {\gamma} for both discounted and average-reward criteria.

Provably Efficient Off-Policy Adversarial Imitation Learning with Convergence Guarantees

Adversarial Imitation Learning (AIL) faces challenges with sample inefficiency because of its reliance on sufficient on-policy data to evaluate the performance of the current policy during reward function updates. In this work, we study the convergence properties and sample complexity of off-policy AIL algorithms. We show that, even in the absence of importance sampling correction, reusing samples generated by the $o(\sqrt{K})$ most recent policies, where $K$ is the number of iterations of policy updates and reward updates, does not undermine the convergence guarantees of this class of algorithms. Furthermore, our results indicate that the distribution shift error induced by off-policy updates is dominated by the benefits of having more data available. This result provides theoretical support for the sample efficiency of off-policy AIL algorithms. To the best of our knowledge, this is the first work that provides theoretical guarantees for off-policy AIL algorithms.

Multiple-policy Evaluation via Density Estimation

In this work, we focus on the multiple-policy evaluation problem where we are given a set of $K$ target policies and the goal is to evaluate their performance (the expected total rewards) to an accuracy $\epsilon$ with probability at least $1-\delta$. We propose an algorithm named $\mathrm{CAESAR}$ to address this problem. Our approach is based on computing an approximate optimal offline sampling distribution and using the data sampled from it to perform the simultaneous estimation of the policy values. $\mathrm{CAESAR}$ consists of two phases. In the first one we produce coarse estimates of the vistation distributions of the target policies at a low order sample complexity rate that scales with $\tilde{O}(\frac{1}{\epsilon})$. In the second phase, we approximate the optimal offline sampling distribution and compute the importance weighting ratios for all target policies by minimizing a step-wise quadratic loss function inspired by the objective in DualDICE. Up to low order and logarithm terms $\mathrm{CAESAR}$ achieves a sample complexity $\tilde{O}\left(\frac{H^4}{\epsilon^2}\sum_{h=1}^H\max_{k\in[K]}\sum_{s,a}\frac{(d_h^{\pi^k}(s,a))^2}{\mu^*_h(s,a)}\right)$, where $d^{\pi}$ is the visitation distribution of policy $\pi$ and $\mu^*$ is the optimal sampling distribution.

Reinforcement Learning-based Receding Horizon Control using Adaptive Control Barrier Functions for Safety-Critical Systems

Optimal control methods provide solutions to safety-critical problems but easily become intractable. Control Barrier Functions (CBFs) have emerged as a popular technique that facilitates their solution by provably guaranteeing safety, through their forward invariance property, at the expense of some performance loss. This approach involves defining a performance objective alongside CBF-based safety constraints that must always be enforced. Unfortunately, both performance and solution feasibility can be significantly impacted by two key factors: (i) the selection of the cost function and associated parameters, and (ii) the calibration of parameters within the CBF-based constraints, which capture the trade-off between performance and conservativeness. %as well as infeasibility. To address these challenges, we propose a Reinforcement Learning (RL)-based Receding Horizon Control (RHC) approach leveraging Model Predictive Control (MPC) with CBFs (MPC-CBF). In particular, we parameterize our controller and use bilevel optimization, where RL is used to learn the optimal parameters while MPC computes the optimal control input. We validate our method by applying it to the challenging automated merging control problem for Connected and Automated Vehicles (CAVs) at conflicting roadways. Results demonstrate improved performance and a significant reduction in the number of infeasible cases compared to traditional heuristic approaches used for tuning CBF-based controllers, showcasing the effectiveness of the proposed method.

One-Shot Averaging for Distributed TD Under Markov Sampling

We consider a distributed setup for reinforcement learning, where each agent has a copy of the same Markov Decision Process but transitions are sampled from the corresponding Markov chain independently by each agent. We show that in this setting, we can achieve a linear speedup for TD($\lambda$), a family of popular methods for policy evaluation, in the sense that $N$ agents can evaluate a policy $N$ times faster provided the target accuracy is small enough. Notably, this speedup is achieved by ``one shot averaging,'' a procedure where the agents run TD($\lambda$) with Markov sampling independently and only average their results after the final step. This significantly reduces the amount of communication required to achieve a linear speedup relative to previous work.

A Model-Based Approach for Improving Reinforcement Learning Efficiency Leveraging Expert Observations

This paper investigates how to incorporate expert observations (without explicit information on expert actions) into a deep reinforcement learning setting to improve sample efficiency. First, we formulate an augmented policy loss combining a maximum entropy reinforcement learning objective with a behavioral cloning loss that leverages a forward dynamics model. Then, we propose an algorithm that automatically adjusts the weights of each component in the augmented loss function. Experiments on a variety of continuous control tasks demonstrate that the proposed algorithm outperforms various benchmarks by effectively utilizing available expert observations.

Smooth Ranking SVM via Cutting-Plane Method

The most popular classification algorithms are designed to maximize classification accuracy during training. However, this strategy may fail in the presence of class imbalance since it is possible to train models with high accuracy by overfitting to the majority class. On the other hand, the Area Under the Curve (AUC) is a widely used metric to compare classification performance of different algorithms when there is a class imbalance, and various approaches focusing on the direct optimization of this metric during training have been proposed. Among them, SVM-based formulations are especially popular as this formulation allows incorporating different regularization strategies easily. In this work, we develop a prototype learning approach that relies on cutting-plane method, similar to Ranking SVM, to maximize AUC. Our algorithm learns simpler models by iteratively introducing cutting planes, thus overfitting is prevented in an unconventional way. Furthermore, it penalizes the changes in the weights at each iteration to avoid large jumps that might be observed in the test performance, thus facilitating a smooth learning process. Based on the experiments conducted on 73 binary classification datasets, our method yields the best test AUC in 25 datasets among its relevant competitors.

On the Performance of Temporal Difference Learning With Neural Networks

Neural Temporal Difference (TD) Learning is an approximate temporal difference method for policy evaluation that uses a neural network for function approximation. Analysis of Neural TD Learning has proven to be challenging. In this paper we provide a convergence analysis of Neural TD Learning with a projection onto $B(\theta_0, \omega)$, a ball of fixed radius $\omega$ around the initial point $\theta_0$. We show an approximation bound of $O(\epsilon) + \tilde{O} (1/\sqrt{m})$ where $\epsilon$ is the approximation quality of the best neural network in $B(\theta_0, \omega)$ and $m$ is the width of all hidden layers in the network.

Adversarial Imitation Learning from Visual Observations using Latent Information

We focus on the problem of imitation learning from visual observations, where the learning agent has access to videos of experts as its sole learning source. The challenges of this framework include the absence of expert actions and the partial observability of the environment, as the ground-truth states can only be inferred from pixels. To tackle this problem, we first conduct a theoretical analysis of imitation learning in partially observable environments. We establish upper bounds on the suboptimality of the learning agent with respect to the divergence between the expert and the agent latent state-transition distributions. Motivated by this analysis, we introduce an algorithm called Latent Adversarial Imitation from Observations, which combines off-policy adversarial imitation techniques with a learned latent representation of the agent's state from sequences of observations. In experiments on high-dimensional continuous robotic tasks, we show that our algorithm matches state-of-the-art performance while providing significant computational advantages. Additionally, we show how our method can be used to improve the efficiency of reinforcement learning from pixels by leveraging expert videos. To ensure reproducibility, we provide free access to our code.