Competitive Facility Location under Random Utilities and Routing Constraints

In this paper, we study a facility location problem within a competitive market context, where customer demand is predicted by a random utility choice model. Unlike prior research, which primarily focuses on simple constraints such as a cardinality constraint on the number of selected locations, we introduce routing constraints that necessitate the selection of locations in a manner that guarantees the existence of a tour visiting all chosen locations while adhering to a specified tour length upper bound. Such routing constraints find crucial applications in various real-world scenarios. The problem at hand features a non-linear objective function, resulting from the utilization of random utilities, together with complex routing constraints, making it computationally challenging. To tackle this problem, we explore three types of valid cuts, namely, outer-approximation and submodular cuts to handle the nonlinear objective function, as well as sub-tour elimination cuts to address the complex routing constraints. These lead to the development of two exact solution methods: a nested cutting plane and nested branch-and-cut algorithms, where these valid cuts are iteratively added to a master problem through two nested loops. We also prove that our nested cutting plane method always converges to optimality after a finite number of iterations. Furthermore, we develop a local search-based metaheuristic tailored for solving large-scale instances and show its pros and cons compared to exact methods. Extensive experiments are conducted on problem instances of varying sizes, demonstrating that our approach excels in terms of solution quality and computation time when compared to other baseline approaches.

SubIQ: Inverse Soft-Q Learning for Offline Imitation with Suboptimal Demonstrations

We consider offline imitation learning (IL), which aims to mimic the expert's behavior from its demonstration without further interaction with the environment. One of the main challenges in offline IL is dealing with the limited support of expert demonstrations that cover only a small fraction of the state-action spaces. In this work, we consider offline IL, where expert demonstrations are limited but complemented by a larger set of sub-optimal demonstrations of lower expertise levels. Most of the existing offline IL methods developed for this setting are based on behavior cloning or distribution matching, where the aim is to match the occupancy distribution of the imitation policy with that of the expert policy. Such an approach often suffers from over-fitting, as expert demonstrations are limited to accurately represent any occupancy distribution. On the other hand, since sub-optimal sets are much larger, there is a high chance that the imitation policy is trained towards sub-optimal policies. In this paper, to address these issues, we propose a new approach based on inverse soft-Q learning, where a regularization term is added to the training objective, with the aim of aligning the learned rewards with a pre-assigned reward function that allocates higher weights to state-action pairs from expert demonstrations, and lower weights to those from lower expertise levels. On standard benchmarks, our inverse soft-Q learning significantly outperforms other offline IL baselines by a large margin.

Imitate the Good and Avoid the Bad: An Incremental Approach to Safe Reinforcement Learning

A popular framework for enforcing safe actions in Reinforcement Learning (RL) is Constrained RL, where trajectory based constraints on expected cost (or other cost measures) are employed to enforce safety and more importantly these constraints are enforced while maximizing expected reward. Most recent approaches for solving Constrained RL convert the trajectory based cost constraint into a surrogate problem that can be solved using minor modifications to RL methods. A key drawback with such approaches is an over or underestimation of the cost constraint at each state. Therefore, we provide an approach that does not modify the trajectory based cost constraint and instead imitates ``good'' trajectories and avoids ``bad'' trajectories generated from incrementally improving policies. We employ an oracle that utilizes a reward threshold (which is varied with learning) and the overall cost constraint to label trajectories as ``good'' or ``bad''. A key advantage of our approach is that we are able to work from any starting policy or set of trajectories and improve on it. In an exhaustive set of experiments, we demonstrate that our approach is able to outperform top benchmark approaches for solving Constrained RL problems, with respect to expected cost, CVaR cost, or even unknown cost constraints.

Inverse Factorized Q-Learning for Cooperative Multi-agent Imitation Learning

This paper concerns imitation learning (IL) (i.e, the problem of learning to mimic expert behaviors from demonstrations) in cooperative multi-agent systems. The learning problem under consideration poses several challenges, characterized by high-dimensional state and action spaces and intricate inter-agent dependencies. In a single-agent setting, IL has proven to be done efficiently through an inverse soft-Q learning process given expert demonstrations. However, extending this framework to a multi-agent context introduces the need to simultaneously learn both local value functions to capture local observations and individual actions, and a joint value function for exploiting centralized learning. In this work, we introduce a novel multi-agent IL algorithm designed to address these challenges. Our approach enables the centralized learning by leveraging mixing networks to aggregate decentralized Q functions. A main advantage of this approach is that the weights of the mixing networks can be trained using information derived from global states. We further establish conditions for the mixing networks under which the multi-agent objective function exhibits convexity within the Q function space. We present extensive experiments conducted on some challenging competitive and cooperative multi-agent game environments, including an advanced version of the Star-Craft multi-agent challenge (i.e., SMACv2), which demonstrates the effectiveness of our proposed algorithm compared to existing state-of-the-art multi-agent IL algorithms.

Mimicking To Dominate: Imitation Learning Strategies for Success in Multiagent Competitive Games

Training agents in multi-agent competitive games presents significant challenges due to their intricate nature. These challenges are exacerbated by dynamics influenced not only by the environment but also by opponents' strategies. Existing methods often struggle with slow convergence and instability. To address this, we harness the potential of imitation learning to comprehend and anticipate opponents' behavior, aiming to mitigate uncertainties with respect to the game dynamics. Our key contributions include: (i) a new multi-agent imitation learning model for predicting next moves of the opponents -- our model works with hidden opponents' actions and local observations; (ii) a new multi-agent reinforcement learning algorithm that combines our imitation learning model and policy training into one single training process; and (iii) extensive experiments in three challenging game environments, including an advanced version of the Star-Craft multi-agent challenge (i.e., SMACv2). Experimental results show that our approach achieves superior performance compared to existing state-of-the-art multi-agent RL algorithms.

Solving Constrained Reinforcement Learning through Augmented State and Reward Penalties

Constrained Reinforcement Learning has been employed to enforce safety constraints on policy through the use of expected cost constraints. The key challenge is in handling expected cost accumulated using the policy and not just in a single step. Existing methods have developed innovative ways of converting this cost constraint over entire policy to constraints over local decisions (at each time step). While such approaches have provided good solutions with regards to objective, they can either be overly aggressive or conservative with respect to costs. This is owing to use of estimates for "future" or "backward" costs in local cost constraints. To that end, we provide an equivalent unconstrained formulation to constrained RL that has an augmented state space and reward penalties. This intuitive formulation is general and has interesting theoretical properties. More importantly, this provides a new paradigm for solving constrained RL problems effectively. As we show in our experimental results, we are able to outperform leading approaches on multiple benchmark problems from literature.

Imitating Opponent to Win: Adversarial Policy Imitation Learning in Two-player Competitive Games

Recent research on vulnerabilities of deep reinforcement learning (RL) has shown that adversarial policies adopted by an adversary agent can influence a target RL agent (victim agent) to perform poorly in a multi-agent environment. In existing studies, adversarial policies are directly trained based on experiences of interacting with the victim agent. There is a key shortcoming of this approach; knowledge derived from historical interactions may not be properly generalized to unexplored policy regions of the victim agent, making the trained adversarial policy significantly less effective. In this work, we design a new effective adversarial policy learning algorithm that overcomes this shortcoming. The core idea of our new algorithm is to create a new imitator to imitate the victim agent's policy while the adversarial policy will be trained not only based on interactions with the victim agent but also based on feedback from the imitator to forecast victim's intention. By doing so, we can leverage the capability of imitation learning in well capturing underlying characteristics of the victim policy only based on sample trajectories of the victim. Our victim imitation learning model differs from prior models as the environment's dynamics are driven by adversary's policy and will keep changing during the adversarial policy training. We provide a provable bound to guarantee a desired imitating policy when the adversary's policy becomes stable. We further strengthen our adversarial policy learning by making our imitator a stronger version of the victim. Finally, our extensive experiments using four competitive MuJoCo game environments show that our proposed adversarial policy learning algorithm outperforms state-of-the-art algorithms.

Weighted Maximum Entropy Inverse Reinforcement Learning

We study inverse reinforcement learning (IRL) and imitation learning (IM), the problems of recovering a reward or policy function from expert's demonstrated trajectories. We propose a new way to improve the learning process by adding a weight function to the maximum entropy framework, with the motivation of having the ability to learn and recover the stochasticity (or the bounded rationality) of the expert policy. Our framework and algorithms allow to learn both a reward (or policy) function and the structure of the entropy terms added to the Markov Decision Processes, thus enhancing the learning procedure. Our numerical experiments using human and simulated demonstrations and with discrete and continuous IRL/IM tasks show that our approach outperforms prior algorithms.

Scalable Distributional Robustness in a Class of Non Convex Optimization with Guarantees

Distributionally robust optimization (DRO) has shown lot of promise in providing robustness in learning as well as sample based optimization problems. We endeavor to provide DRO solutions for a class of sum of fractionals, non-convex optimization which is used for decision making in prominent areas such as facility location and security games. In contrast to previous work, we find it more tractable to optimize the equivalent variance regularized form of DRO rather than the minimax form. We transform the variance regularized form to a mixed-integer second order cone program (MISOCP), which, while guaranteeing near global optimality, does not scale enough to solve problems with real world data-sets. We further propose two abstraction approaches based on clustering and stratified sampling to increase scalability, which we then use for real world data-sets. Importantly, we provide near global optimality guarantees for our approach and show experimentally that our solution quality is better than the locally optimal ones achieved by state-of-the-art gradient-based methods. We experimentally compare our different approaches and baselines, and reveal nuanced properties of a DRO solution.

Robust Entropy-regularized Markov Decision Processes

Stochastic and soft optimal policies resulting from entropy-regularized Markov decision processes (ER-MDP) are desirable for exploration and imitation learning applications. Motivated by the fact that such policies are sensitive with respect to the state transition probabilities, and the estimation of these probabilities may be inaccurate, we study a robust version of the ER-MDP model, where the stochastic optimal policies are required to be robust with respect to the ambiguity in the underlying transition probabilities. Our work is at the crossroads of two important schemes in reinforcement learning (RL), namely, robust MDP and entropy regularized MDP. We show that essential properties that hold for the non-robust ER-MDP and robust unregularized MDP models also hold in our settings, making the robust ER-MDP problem tractable. We show how our framework and results can be integrated into different algorithmic schemes including value or (modified) policy iteration, which would lead to new robust RL and inverse RL algorithms to handle uncertainties. Analyses on computational complexity and error propagation under conventional uncertainty settings are also provided.