arXiv subjects

Mukesh Ghimire

Publications and source records attributed to Mukesh Ghimire.

11 recordsLinked to original sources

arXiv2026

Fast Strategy Solving for the Informed Player in Two-Player Zero-Sum Linear-Quadratic Differential Games with One-Sided Information

We study finite-horizon two-player zero-sum differential games with one-sided payoff information ($G$), where the informed player (P1) knows the game payoff, while P2 only has a public belief over a finite set of possible payoffs. In this case, P1's Nash equilibrium (NE) behavioral strategy may control the release of the type information or even resort to manipulate P2's belief. Previous studies revealed an atomic structure of the NE of $G$ with general nonlinear dynamics and payoffs, leading to tractable NE approximation. Implementing such approximation schemes for real-time sub-game solving, however, has not been achieved, yet is desired for applications where sim-to-real gaps exist and robust control is required. This paper improves the computational efficiency of sub-game solving for P1 during $G$ with linear dynamics and quadratic losses. Specifically, we show that P1's NE computation can be formulated as a bi-level optimization problem where the outer level optimizes the "signaling" strategy, i.e., when and how to reveal information through control, and the inner level is a game-tree LQR that solves for the optimal closed-loop control. This bi-level problem is solved via an adjoint-enabled backpropagation scheme: A "backward" LQR pass is followed by a "forward" gradient descent pass for improving the signaling. We apply the proposed algorithm to approximate NEs for variants of a homing problem with a 8D state space, 2D action spaces, and a discrete time horizon of $K=10$. The algorithm achieves $\approx$10Hz sub-game solving, enabling robust game-theoretic planning under information asymmetry and random disturbances.

cs.GT↗

arXiv2026

PRISM: A Unified Framework for Post-Training LLMs Without Verifiable Rewards

Current techniques for post-training Large Language Models (LLMs) rely either on costly human supervision or on external verifiers to boost performance on tasks such as mathematical reasoning and code generation. However, as LLMs improve their problem-solving, any further improvement will potentially require high-quality solutions to difficult problems that are not available to humans. As a result, learning from unlabeled data is becoming increasingly attractive in the research community. Existing methods extract learning signal from a model's consistency, either by majority voting or by converting the model's internal confidence into reward. Although internal consistency metric such as entropy or self-certainty require no human intervention, as we show in this work, these are unreliable signals for large-scale and long-term training. To address the unreliability, we propose PRISM, a unified training framework that uses a Process Reward Model (PRM) to guide learning alongside model's internal confidence in the absence of ground-truth labels. We show that effectively combining PRM with self-certainty can lead to both stable training and better test-time performance, and also keep the model's internal confidence in check. Code available at https://github.com/ghimiremukesh/PRISM.

cs.CL↗

arXiv2025

Parametric Value Approximation for General-sum Differential Games with State Constraints

General-sum differential games can approximate values solved by Hamilton-Jacobi-Isaacs (HJI) equations for efficient inference when information is incomplete. However, solving such games through conventional methods encounters the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a scalable approach to alleviate the CoD and approximate values, but there exist convergence issues for value approximations through vanilla PINNs when state constraints lead to values with large Lipschitz constants, particularly in safety-critical applications. In addition to addressing CoD, it is necessary to learn a generalizable value across a parametric space of games, rather than training multiple ones for each specific player-type configuration. To overcome these challenges, we propose a Hybrid Neural Operator (HNO), which is an operator that can map parameter functions for games to value functions. HNO leverages informative supervised data and samples PDE-driven data across entire spatial-temporal space for model refinement. We evaluate HNO on 9D and 13D scenarios with nonlinear dynamics and state constraints, comparing it against a Supervised Neural Operator (a variant of DeepONet). Under the same computational budget and training data, HNO outperforms SNO for safety performance. This work provides a step toward scalable and generalizable value function approximation, enabling real-time inference for complex human-robot or multi-agent interactions.

cs.RO↗

arXiv2025

Two-Player Zero-Sum Differential Games with One-Sided Information

Unlike Poker where the action space $\mathcal{A}$ is discrete, differential games in the physical world often have continuous action spaces not amenable to discrete abstraction, rendering no-regret algorithms with $\mathcal{O}(|\mathcal{A}|)$ complexity not scalable. To address this challenge within the scope of two-player zero-sum (2p0s) games with one-sided information, we show that (1) a computational complexity independent of $|\mathcal{A}|$ can be achieved by exploiting the convexification property of incomplete-information games and the Isaacs' condition that commonly holds for dynamical systems, and that (2) the computation of the two equilibrium strategies can be decoupled under one-sidedness of information. Leveraging these insights, we develop an algorithm that successfully approximates the optimal strategy in a homing game. Code available in https://github.com/ghimiremukesh/cams/tree/workshop

cs.GT↗

arXiv2025

Solving Football by Exploiting Equilibrium Structure of 2p0s Differential Games with One-Sided Information

For a two-player imperfect-information extensive-form game (IIEFG) with $K$ time steps and a player action space of size $U$, the game tree complexity is $U^{2K}$, causing existing IIEFG solvers to struggle with large or infinite $(U,K)$, e.g., differential games with continuous action spaces. To partially address this scalability challenge, we focus on an important class of 2p0s games where the informed player (P1) knows the payoff while the uninformed player (P2) only has a belief over the set of $I$ possible payoffs. Such games encompass a wide range of scenarios in sports, defense, cybersecurity, and finance. We prove that under mild conditions, P1's (resp. P2's) equilibrium strategy at any infostate concentrates on at most $I$ (resp. $I+1$) action prototypes. When $I\ll U$, this equilibrium structure causes the game tree complexity to collapse to $I^K$ for P1 when P2 plays best responses, and $(I+1)^K$ for P2 in a dual game where P1 plays best responses. We then show that exploiting this structure in model-free multiagent reinforcement learning and model predictive control leads to significant improvements in learning accuracy and efficiency from SOTA IIEFG solvers. Our demonstration solves a 22-player football game with continuous action spaces and $K=10$ time steps, where the offense team needs to strategically conceal their play until a critical moment in order to exploit information advantage. Code is available at https://github.com/ghimiremukesh/cams/tree/iclr

cs.GT↗

arXiv2024

State-Constrained Zero-Sum Differential Games with One-Sided Information

We study zero-sum differential games with state constraints and one-sided information, where the informed player (Player 1) has a categorical payoff type unknown to the uninformed player (Player 2). The goal of Player 1 is to minimize his payoff without violating the constraints, while that of Player 2 is to violate the state constraints if possible, or to maximize the payoff otherwise. One example of the game is a man-to-man matchup in football. Without state constraints, Cardaliaguet (2007) showed that the value of such a game exists and is convex to the common belief of players. Our theoretical contribution is an extension of this result to games with state constraints and the derivation of the primal and dual subdynamic principles necessary for computing behavioral strategies. Different from existing works that are concerned about the scalability of no-regret learning in games with discrete dynamics, our study reveals the underlying structure of strategies for belief manipulation resulting from information asymmetry and state constraints. This structure will be necessary for scalable learning on games with continuous actions and long time windows. We use a simplified football game to demonstrate the utility of this work, where we reveal player positions and belief states in which the attacker should (or should not) play specific random deceptive moves to take advantage of information asymmetry, and compute how the defender should respond.

cs.GT↗

arXiv2024

Pontryagin Neural Operator for Solving Parametric General-Sum Differential Games

The values of two-player general-sum differential games are viscosity solutions to Hamilton-Jacobi-Isaacs (HJI) equations. Value and policy approximations for such games suffer from the curse of dimensionality (CoD). Alleviating CoD through physics-informed neural networks (PINN) encounters convergence issues when differentiable values with large Lipschitz constants are present due to state constraints. On top of these challenges, it is often necessary to learn generalizable values and policies across a parametric space of games, e.g., for game parameter inference when information is incomplete. To address these challenges, we propose in this paper a Pontryagin-mode neural operator that outperforms the current state-of-the-art hybrid PINN model on safety performance across games with parametric state constraints. Our key contribution is the introduction of a costate loss defined on the discrepancy between forward and backward costate rollouts, which are computationally cheap. We show that the costate dynamics, which can reflect state constraint violation, effectively enables the learning of differentiable values with large Lipschitz constants, without requiring manually supervised data as suggested by the hybrid PINN model. More importantly, we show that the close relationship between costates and policies makes the former critical in learning feedback control policies with generalizable safety performance.

cs.LG↗

arXiv2024

Value Approximation for Two-Player General-Sum Differential Games with State Constraints

Solving Hamilton-Jacobi-Isaacs (HJI) PDEs numerically enables equilibrial feedback control in two-player differential games, yet faces the curse of dimensionality (CoD). While physics-informed neural networks (PINNs) have shown promise in alleviating CoD in solving PDEs, vanilla PINNs fall short in learning discontinuous solutions due to their sampling nature, leading to poor safety performance of the resulting policies when values are discontinuous due to state or temporal logic constraints. In this study, we explore three potential solutions to this challenge: (1) a hybrid learning method that is guided by both supervisory equilibria and the HJI PDE, (2) a value-hardening method where a sequence of HJIs are solved with increasing Lipschitz constant on the constraint violation penalty, and (3) the epigraphical technique that lifts the value to a higher dimensional state space where it becomes continuous. Evaluations through 5D and 9D vehicle and 13D drone simulations reveal that the hybrid method outperforms others in terms of generalization and safety performance by taking advantage of both the supervisory equilibrium values and costates, and the low cost of PINN loss gradients.

cs.RO↗

arXiv2023

Solving Two-Player General-Sum Games Between Swarms

Hamilton-Jacobi-Isaacs (HJI) PDEs are the governing equations for the two-player general-sum games. Unlike Reinforcement Learning (RL) methods, which are data-intensive methods for learning value function, learning HJ PDEs provide a guaranteed convergence to the Nash Equilibrium value of the game when it exists. However, a caveat is that solving HJ PDEs becomes intractable when the state dimension increases. To circumvent the curse of dimensionality (CoD), physics-informed machine learning methods with supervision can be used and have been shown to be effective in generating equilibrial policies in two-player general-sum games. In this work, we extend the existing work on agent-level two-player games to a two-player swarm-level game, where two sub-swarms play a general-sum game. We consider the \textit{Kolmogorov forward equation} as the dynamic model for the evolution of the densities of the swarms. Results show that policies generated from the physics-informed neural network (PINN) result in a higher payoff than a Nash Double Deep Q-Network (Nash DDQN) agent and have comparable performance with numerical solvers.

cs.MA↗

arXiv2023

Approximating Discontinuous Nash Equilibrial Values of Two-Player General-Sum Differential Games

Finding Nash equilibrial policies for two-player differential games requires solving Hamilton-Jacobi-Isaacs (HJI) PDEs. Self-supervised learning has been used to approximate solutions of such PDEs while circumventing the curse of dimensionality. However, this method fails to learn discontinuous PDE solutions due to its sampling nature, leading to poor safety performance of the resulting controllers in robotics applications when player rewards are discontinuous. This paper investigates two potential solutions to this problem: a hybrid method that leverages both supervised Nash equilibria and the HJI PDE, and a value-hardening method where a sequence of HJIs are solved with a gradually hardening reward. We compare these solutions using the resulting generalization and safety performance in two vehicle interaction simulation studies with 5D and 9D state spaces, respectively. Results show that with informative supervision (e.g., collision and near-collision demonstrations) and the low cost of self-supervised learning, the hybrid method achieves better safety performance than the supervised, self-supervised, and value hardening approaches on equal computational budget. Value hardening fails to generalize in the higher-dimensional case without informative supervision. Lastly, we show that the neural activation function needs to be continuously differentiable for learning PDEs and its choice can be case dependent.

cs.LG↗

arXiv2021

Lane Change Decision-Making through Deep Reinforcement Learning

Due to the complexity and volatility of the traffic environment, decision-making in autonomous driving is a significantly hard problem. In this project, we use a Deep Q-Network, along with rule-based constraints to make lane-changing decision. A safe and efficient lane change behavior may be obtained by combining high-level lateral decision-making with low-level rule-based trajectory monitoring. The agent is anticipated to perform appropriate lane-change maneuvers in a real-world-like udacity simulator after training it for a total of 100 episodes. The results shows that the rule-based DQN performs better than the DQN method. The rule-based DQN achieves a safety rate of 0.8 and average speed of 47 MPH

cs.RO↗