arXiv subjects

David Fridovich-Keil

Publications and source records attributed to David Fridovich-Keil.

At least 91 records · Page 5Linked to original sources

arXiv2024

Hierarchical Control for Cooperative Teams in Competitive Autonomous Racing

We investigate the problem of autonomous racing among teams of cooperative agents that are subject to realistic racing rules. Our work extends previous research on hierarchical control in head-to-head autonomous racing by considering a generalized version of the problem while maintaining the two-level hierarchical control structure. A high-level tactical planner constructs a discrete game that encodes the complex rules using simplified dynamics to produce a sequence of target waypoints. The low-level path planner uses these waypoints as a reference trajectory and computes high-resolution control inputs by solving a simplified formulation of a racing game with a simplified representation of the realistic racing rules. We explore two approaches for the low-level path planner: training a multi-agent reinforcement learning (MARL) policy and solving a linear-quadratic Nash game (LQNG) approximation. We evaluate our controllers on simple and complex tracks against three baselines: an end-to-end MARL controller, a MARL controller tracking a fixed racing line, and an LQNG controller tracking a fixed racing line. Quantitative results show our hierarchical methods outperform the baselines in terms of race wins, overall team performance, and compliance with the rules. Qualitatively, we observe the hierarchical controllers mimic actions performed by expert human drivers such as coordinated overtaking, defending against multiple opponents, and long-term planning for delayed advantages.

cs.MA↗

arXiv2024

Hierarchical Control for Head-to-Head Autonomous Racing

We develop a hierarchical controller for head-to-head autonomous racing. We first introduce a formulation of a racing game with realistic safety and fairness rules. A high-level planner approximates the original formulation as a discrete game with simplified state, control, and dynamics to easily encode the complex safety and fairness rules and calculates a series of target waypoints. The low-level controller takes the resulting waypoints as a reference trajectory and computes high-resolution control inputs by solving an alternative formulation approximation with simplified objectives and constraints. We consider two approaches for the low-level planner, constructing two hierarchical controllers. One approach uses multi-agent reinforcement learning (MARL), and the other solves a linear-quadratic Nash game (LQNG) to produce control inputs. The controllers are compared against three baselines: an end-to-end MARL controller, a MARL controller tracking a fixed racing line, and an LQNG controller tracking a fixed racing line. Quantitative results show that the proposed hierarchical methods outperform their respective baseline methods in terms of head-to-head race wins and abiding by the rules. The hierarchical controller using MARL for low-level control consistently outperformed all other methods by winning over 90% of head-to-head races and more consistently adhered to the complex racing rules. Qualitatively, we observe the proposed controllers mimicking actions performed by expert human drivers such as shielding/blocking, overtaking, and long-term planning for delayed advantages. We show that hierarchical planning for game-theoretic reasoning produces competitive behavior even when challenged with complex rules and constraints.

cs.MA↗

arXiv2024

Relationship Design for Socially-Aware Behavior in Static Games

Autonomous agents can adopt socially-aware behaviors to reduce social costs, mimicking the way animals interact in nature and humans in society. We present a new approach to model socially-aware decision-making that includes two key elements: bounded rationality and inter-agent relationships. We capture the interagent relationships by introducing a novel model called a relationship game and encode agents' bounded rationality using quantal response equilibria. For each relationship game, we define a social cost function and formulate a mechanism design problem to optimize weights for relationships that minimize social cost at the equilibrium. We address the multiplicity of equilibria by presenting the problem in two forms: Min-Max and Min-Min, aimed respectively at minimization of the highest and lowest social costs in the equilibria. We compute the quantal response equilibrium by solving a least-squares problem defined with its Karush-Kuhn-Tucker conditions, and propose two projected gradient descent algorithms to solve the mechanism design problems. Numerical results, including two-lane congestion and congestion with an ambulance, confirm that these algorithms consistently reach the equilibrium with the intended social costs.

cs.MA↗

arXiv2023

Contingency Games for Multi-Agent Interaction

Contingency planning, wherein an agent generates a set of possible plans conditioned on the outcome of an uncertain event, is an increasingly popular way for robots to act under uncertainty. In this work we take a game-theoretic perspective on contingency planning, tailored to multi-agent scenarios in which a robot's actions impact the decisions of other agents and vice versa. The resulting contingency game allows the robot to efficiently interact with other agents by generating strategic motion plans conditioned on multiple possible intents for other actors in the scene. Contingency games are parameterized via a scalar variable which represents a future time when intent uncertainty will be resolved. By estimating this parameter online, we construct a game-theoretic motion planner that adapts to changing beliefs while anticipating future certainty. We show that existing variants of game-theoretic planning under uncertainty are readily obtained as special cases of contingency games. Through a series of simulated autonomous driving scenarios, we demonstrate that contingency games close the gap between certainty-equivalent games that commit to a single hypothesis and non-contingent multi-hypothesis games that do not account for future uncertainty reduction.

cs.RO↗

arXiv2023

An Investigation of Time Reversal Symmetry in Reinforcement Learning

One of the fundamental challenges associated with reinforcement learning (RL) is that collecting sufficient data can be both time-consuming and expensive. In this paper, we formalize a concept of time reversal symmetry in a Markov decision process (MDP), which builds upon the established structure of dynamically reversible Markov chains (DRMCs) and time-reversibility in classical physics. Specifically, we investigate the utility of this concept in reducing the sample complexity of reinforcement learning. We observe that utilizing the structure of time reversal in an MDP allows every environment transition experienced by an agent to be transformed into a feasible reverse-time transition, effectively doubling the number of experiences in the environment. To test the usefulness of this newly synthesized data, we develop a novel approach called time symmetric data augmentation (TSDA) and investigate its application in both proprioceptive and pixel-based state within the realm of off-policy, model-free RL. Empirical evaluations showcase how these synthetic transitions can enhance the sample efficiency of RL agents in time reversible scenarios without friction or contact. We also test this method in more realistic environments where these assumptions are not globally satisfied. We find that TSDA can significantly degrade sample efficiency and policy performance, but can also improve sample efficiency under the right conditions. Ultimately we conclude that time symmetry shows promise in enhancing the sample efficiency of reinforcement learning and provide guidance when the environment and reward structures are of an appropriate form for TSDA to be employed effectively.

cs.LG↗

arXiv2023

The Computation of Approximate Generalized Feedback Nash Equilibria

We present the concept of a Generalized Feedback Nash Equilibrium (GFNE) in dynamic games, extending the Feedback Nash Equilibrium concept to games in which players are subject to state and input constraints. We formalize necessary and sufficient conditions for (local) GFNE solutions at the trajectory level, which enable the development of efficient numerical methods for their computation. Specifically, we propose a Newton-style method for finding game trajectories which satisfy necessary conditions for an equilibrium, which can then be checked against sufficiency conditions. We show that the evaluation of the necessary conditions in general requires computing a series of nested, implicitly-defined derivatives, which quickly becomes intractable. To this end, we introduce an approximation to the necessary conditions which is amenable to efficient evaluation, and in turn, computation of solutions. We term the solutions to the approximate necessary conditions Generalized Feedback Quasi-Nash Equilibria (GFQNE), and we introduce numerical methods for their computation. In particular, we develop a Sequential Linear-Quadratic Game approach, in which a LQ local approximation of the game is solved at each iteration. The development of this method relies on the ability to compute a GFNE to inequality- and equality-constrained LQ games, and therefore specific methods for the solution of these special cases are developed in detail. We demonstrate the effectiveness of the proposed solution approach on a dynamic game arising in an autonomous driving application.

math.OC↗

arXiv2023

Learning Hyperplanes for Multi-Agent Collision Avoidance in Space

A core challenge of multi-robot interactions is collision avoidance among robots with potentially conflicting objectives. We propose a game-theoretic method for collision avoidance based on rotating hyperplane constraints. These constraints ensure collision avoidance by defining separating hyperplanes that rotate around a keep-out zone centered on certain robots. Since it is challenging to select the parameters that define a hyperplane without introducing infeasibilities, we propose to learn them from an expert trajectory i.e., one collected by recording human operators. To do so, we solve for the parameters whose corresponding equilibrium trajectory best matches the expert trajectory. We validate our method by learning hyperplane parameters from noisy expert trajectories and demonstrate the generalizability of the learned parameters to scenarios with more robots and previously unseen initial conditions.

cs.RO↗

arXiv2023

Enabling Efficient, Reliable Real-World Reinforcement Learning with Approximate Physics-Based Models

We focus on developing efficient and reliable policy optimization strategies for robot learning with real-world data. In recent years, policy gradient methods have emerged as a promising paradigm for training control policies in simulation. However, these approaches often remain too data inefficient or unreliable to train on real robotic hardware. In this paper we introduce a novel policy gradient-based policy optimization framework which systematically leverages a (possibly highly simplified) first-principles model and enables learning precise control policies with limited amounts of real-world data. Our approach $1)$ uses the derivatives of the model to produce sample-efficient estimates of the policy gradient and $2)$ uses the model to design a low-level tracking controller, which is embedded in the policy class. Theoretical analysis provides insight into how the presence of this feedback controller overcomes key limitations of stand-alone policy gradient methods, while hardware experiments with a small car and quadruped demonstrate that our approach can learn precise control strategies reliably and with only minutes of real-world data.

cs.LG↗

arXiv2023

Connected Autonomous Vehicle Motion Planning with Video Predictions from Smart, Self-Supervised Infrastructure

Connected autonomous vehicles (CAVs) promise to enhance safety, efficiency, and sustainability in urban transportation. However, this is contingent upon a CAV correctly predicting the motion of surrounding agents and planning its own motion safely. Doing so is challenging in complex urban environments due to frequent occlusions and interactions among many agents. One solution is to leverage smart infrastructure to augment a CAV's situational awareness; the present work leverages a recently proposed "Self-Supervised Traffic Advisor" (SSTA) framework of smart sensors that teach themselves to generate and broadcast useful video predictions of road users. In this work, SSTA predictions are modified to predict future occupancy instead of raw video, which reduces the data footprint of broadcast predictions. The resulting predictions are used within a planning framework, demonstrating that this design can effectively aid CAV motion planning. A variety of numerical experiments study the key factors that make SSTA outputs useful for practical CAV planning in crowded urban environments.

cs.RO↗

arXiv2023

Soft-Bellman Equilibrium in Affine Markov Games: Forward Solutions and Inverse Learning

Markov games model interactions among multiple players in a stochastic, dynamic environment. Each player in a Markov game maximizes its expected total discounted reward, which depends upon the policies of the other players. We formulate a class of Markov games, termed affine Markov games, where an affine reward function couples the players' actions. We introduce a novel solution concept, the soft-Bellman equilibrium, where each player is boundedly rational and chooses a soft-Bellman policy rather than a purely rational policy as in the well-known Nash equilibrium concept. We provide conditions for the existence and uniqueness of the soft-Bellman equilibrium and propose a nonlinear least-squares algorithm to compute such an equilibrium in the forward problem. We then solve the inverse game problem of inferring the players' reward parameters from observed state-action trajectories via a projected-gradient algorithm. Experiments in a predator-prey OpenAI Gym environment show that the reward parameters inferred by the proposed algorithm outperform those inferred by a baseline algorithm: they reduce the Kullback-Leibler divergence between the equilibrium policies and observed policies by at least two orders of magnitude.

cs.GT↗

arXiv2023

Risk-Minimizing Two-Player Zero-Sum Stochastic Differential Game via Path Integral Control

This paper addresses a continuous-time risk-minimizing two-player zero-sum stochastic differential game (SDG), in which each player aims to minimize its probability of failure. Failure occurs in the event when the state of the game enters into predefined undesirable domains, and one player's failure is the other's success. We derive a sufficient condition for this game to have a saddle-point equilibrium and show that it can be solved via a Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE) with Dirichlet boundary condition. Under certain assumptions on the system dynamics and cost function, we establish the existence and uniqueness of the saddle-point of the game. We provide explicit expressions for the saddle-point policies which can be numerically evaluated using path integral control. This allows us to solve the game online via Monte Carlo sampling of system trajectories. We implement our control synthesis framework on two classes of risk-minimizing zero-sum SDGs: a disturbance attenuation problem and a pursuit-evasion game. Simulation studies are presented to validate the proposed control synthesis framework.

math.OC↗

arXiv2023

Cost Design in Atomic Routing Games

An atomic routing game is a multiplayer game on a directed graph. Each player in the game chooses a path -- a sequence of links that connect its origin node to its destination node -- with the lowest cost, where the cost of each link is a function of all players' choices. We develop a novel numerical method to design the link cost function in atomic routing games such that the players' choices at the Nash equilibrium minimize a given smooth performance function. This method first approximates the nonsmooth Nash equilibrium conditions with smooth ones, then iteratively improves the link cost function via implicit differentiation. We demonstrate the application of this method to atomic routing games that model noncooperative agents navigating in grid worlds.

cs.GT↗

arXiv2023

Online and Offline Learning of Player Objectives from Partial Observations in Dynamic Games

Robots deployed to the real world must be able to interact with other agents in their environment. Dynamic game theory provides a powerful mathematical framework for modeling scenarios in which agents have individual objectives and interactions evolve over time. However, a key limitation of such techniques is that they require a-priori knowledge of all players' objectives. In this work, we address this issue by proposing a novel method for learning players' objectives in continuous dynamic games from noise-corrupted, partial state observations. Our approach learns objectives by coupling the estimation of unknown cost parameters of each player with inference of unobserved states and inputs through Nash equilibrium constraints. By coupling past state estimates with future state predictions, our approach is amenable to simultaneous online learning and prediction in receding horizon fashion. We demonstrate our method in several simulated traffic scenarios in which we recover players' preferences for, e.g., desired travel speed and collision-avoidance behavior. Results show that our method reliably estimates game-theoretic models from noise-corrupted data that closely matches ground-truth objectives, consistently outperforming state-of-the-art approaches.

cs.RO↗

arXiv2023

Robust Forecasting for Robotic Control: A Game-Theoretic Approach

Modern robots require accurate forecasts to make optimal decisions in the real world. For example, self-driving cars need an accurate forecast of other agents' future actions to plan safe trajectories. Current methods rely heavily on historical time series to accurately predict the future. However, relying entirely on the observed history is problematic since it could be corrupted by noise, have outliers, or not completely represent all possible outcomes. To solve this problem, we propose a novel framework for generating robust forecasts for robotic control. In order to model real-world factors affecting future forecasts, we introduce the notion of an adversary, which perturbs observed historical time series to increase a robot's ultimate control cost. Specifically, we model this interaction as a zero-sum two-player game between a robot's forecaster and this hypothetical adversary. We show that our proposed game may be solved to a local Nash equilibrium using gradient-based optimization techniques. Furthermore, we show that a forecaster trained with our method performs 30.14% better on out-of-distribution real-world lane change data than baselines.

cs.RO↗

arXiv2023

GrAVITree: Graph-based Approximate Value Function In a Tree

In this paper, we introduce GrAVITree, a tree- and sampling-based algorithm to compute a near-optimal value function and corresponding feedback policy for indefinite time-horizon, terminal state-constrained nonlinear optimal control problems. Our algorithm is suitable for arbitrary nonlinear control systems with both state and input constraints. The algorithm works by sampling feasible control inputs and branching backwards in time from the terminal state to build the tree, thereby associating each vertex in the tree with a feasible control sequence to reach the terminal state. Additionally, we embed this stochastic tree within a larger graph structure, rewiring of which enables rapid adaptation to changes in problem structure due to, e.g., newly detected obstacles. Because our method reasons about global problem structure without relying on (potentially imprecise) derivative information, it is particularly well suited to controlling a system based on an imperfect deep neural network model of its dynamics. We demonstrate this capability in the context of an inverted pendulum, where we use a learned model of the pendulum with actuator limits and achieve robust stabilization in settings where competing graph-based and derivative-based techniques fail.

eess.SY↗

arXiv2023

Cost Inference for Feedback Dynamic Games from Noisy Partial State Observations and Incomplete Trajectories

In multi-agent dynamic games, the Nash equilibrium state trajectory of each agent is determined by its cost function and the information pattern of the game. However, the cost and trajectory of each agent may be unavailable to the other agents. Prior work on using partial observations to infer the costs in dynamic games assumes an open-loop information pattern. In this work, we demonstrate that the feedback Nash equilibrium concept is more expressive and encodes more complex behavior. It is desirable to develop specific tools for inferring players' objectives in feedback games. Therefore, we consider the dynamic game cost inference problem under the feedback information pattern, using only partial state observations and incomplete trajectory data. To this end, we first propose an inverse feedback game loss function, whose minimizer yields a feedback Nash equilibrium state trajectory closest to the observation data. We characterize the landscape and differentiability of the loss function. Given the difficulty of obtaining the exact gradient, our main contribution is an efficient gradient approximator, which enables a novel inverse feedback game solver that minimizes the loss using first-order optimization. In thorough empirical evaluations, we demonstrate that our algorithm converges reliably and has better robustness and generalization performance than the open-loop baseline method when the observation data reflects a group of players acting in a feedback Nash game.

cs.MA↗

arXiv2022

Alternating Direction Method of Multipliers for Decomposable Saddle-Point Problems

Saddle-point problems appear in various settings including machine learning, zero-sum stochastic games, and regression problems. We consider decomposable saddle-point problems and study an extension of the alternating direction method of multipliers to such saddle-point problems. Instead of solving the original saddle-point problem directly, this algorithm solves smaller saddle-point problems by exploiting the decomposable structure. We show the convergence of this algorithm for convex-concave saddle-point problems under a mild assumption. We also provide a sufficient condition for which the assumption holds. We demonstrate the convergence properties of the saddle-point alternating direction method of multipliers with numerical examples on a power allocation problem in communication channels and a network routing problem with adversarial costs.

math.OC↗

arXiv2022

Inverse Matrix Games with Unique Quantal Response Equilibrium

In an inverse game problem, one needs to infer the cost function of the players in a game such that a desired joint strategy is a Nash equilibrium. We study the inverse game problem for a class of multiplayer matrix games, where the cost perceived by each player is corrupted by random noise. We provide sufficient conditions for the players' quantal response equilibrium -- a generalization of the Nash equilibrium to games with perception noise -- to be unique. We develop efficient optimization algorithms for inferring the cost matrix based on semidefinite programs and bilevel optimization. We demonstrate the application of these methods in encouraging collision avoidance and fair resource allocation.

cs.GT↗