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Source author record

Maryam Kamgarpour

Maryam Kamgarpour appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
math.OCSystems and ControlMachine LearningMultiagent SystemsArtificial IntelligenceComputer Science and Game Theoryeess.SYmath.COmath.NANumerical AnalysisRobotics

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Published work

23 published item(s)

preprint2026arXiv

Fast Rates for Inverse Reinforcement Learning

We establish novel structural and statistical results for entropy-regularized min-max inverse reinforcement learning (Min-Max-IRL) with linear reward classes in finite-horizon MDPs with Borel state and action spaces. On the structural side, we show that maximum likelihood estimation (MLE) and Min-Max-IRL are equivalent at the population level, and at the empirical level under deterministic dynamics. On the statistical side, exploiting pseudo-self-concordance of the Min-Max-IRL loss, we prove that both the trajectory-level KL divergence and the squared parameter error in the Hessian norm decay at the fast rate $\mathcal{O}(n^{-1})$, where $n$ is the number of expert trajectories. Our guarantees apply under misspecification and require no exploration assumptions. We further extend reward-identifiability results to general Borel spaces and derive novel results on the derivatives of the soft-optimal value function with respect to reward parameters.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Finite-time convergence to an $ε$-efficient Nash equilibrium in potential games

This paper investigates the convergence time of log-linear learning to an $ε$-efficient Nash equilibrium in potential games, where an efficient Nash equilibrium is defined as the maximizer of the potential function. Previous literature provides asymptotic convergence rates to efficient Nash equilibria, and existing finite-time rates are limited to potential games with further assumptions such as the interchangeability of players. We prove the first finite-time convergence to an $ε$-efficient Nash equilibrium in general potential games. Our bounds depend polynomially on $1/ε$, an improvement over previous bounds for subclasses of potential games that are exponential in $1/ε$. We then strengthen our convergence result in two directions: first, we show that a variant of log-linear learning requiring a constant factor less feedback on the utility per round enjoys a similar convergence time; second, we demonstrate the robustness of our convergence guarantee if log-linear learning is subject to small perturbations such as alterations in the learning rule or noise-corrupted utilities.

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preprint2026arXiv

Independent Learning of Nash Equilibria in Partially Observable Markov Potential Games with Decoupled Dynamics

We study Nash equilibrium learning in partially observable Markov games (POMGs), a multi-agent reinforcement learning framework in which agents cannot fully observe the underlying state. Prior work in this setting relies on centralization or information sharing, and suffers from sample and computational complexity that scales exponentially in the number of players. We focus on a subclass of POMGs with independent state transitions, where agents remain coupled through their rewards, and assume that the underlying fully observed Markov game is a Markov potential game. For this class, we present an independent learning algorithm in which players, observing only their own actions and observations and without communication, jointly converge to an approximate Nash equilibrium. Due to partial observability, optimal policies may in general depend on the full action-observation history. Under a filter stability assumption, we show that policies based on finite history windows provide sufficient approximation guarantees. This enables us to approximate the POMG by a surrogate Markov game that is near-potential, leading to quasi-polynomial sample and computational complexity for independent Nash equilibrium learning in the underlying POMG.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Efficient Model-based Multi-agent Reinforcement Learning via Optimistic Equilibrium Computation

We consider model-based multi-agent reinforcement learning, where the environment transition model is unknown and can only be learned via expensive interactions with the environment. We propose H-MARL (Hallucinated Multi-Agent Reinforcement Learning), a novel sample-efficient algorithm that can efficiently balance exploration, i.e., learning about the environment, and exploitation, i.e., achieve good equilibrium performance in the underlying general-sum Markov game. H-MARL builds high-probability confidence intervals around the unknown transition model and sequentially updates them based on newly observed data. Using these, it constructs an optimistic hallucinated game for the agents for which equilibrium policies are computed at each round. We consider general statistical models (e.g., Gaussian processes, deep ensembles, etc.) and policy classes (e.g., deep neural networks), and theoretically analyze our approach by bounding the agents' dynamic regret. Moreover, we provide a convergence rate to the equilibria of the underlying Markov game. We demonstrate our approach experimentally on an autonomous driving simulation benchmark. H-MARL learns successful equilibrium policies after a few interactions with the environment and can significantly improve the performance compared to non-optimistic exploration methods.

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preprint2022arXiv

On the Rate of Convergence of Payoff-based Algorithms to Nash Equilibrium in Strongly Monotone Games

We derive the rate of convergence to Nash equilibria for the payoff-based algorithm proposed in \cite{tat_kam_TAC}. These rates are achieved under the standard assumption of convexity of the game, strong monotonicity and differentiability of the pseudo-gradient. In particular, we show the algorithm achieves $O(\frac{1}{T})$ in the two-point function evaluating setting and $O(\frac{1}{\sqrt{T}})$ in the one-point function evaluation under additional requirement of Lipschitz continuity of the pseudo-gradient. These rates are to our knowledge the best known rates for the corresponding problem classes.

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preprint2022arXiv

System-level, Input-output and New Parameterizations of Stabilizing Controllers, and Their Numerical Computation

It is known that the set of internally stabilizing controller $\mathcal{C}_{\text{stab}}$ is non-convex, but it admits convex characterizations using certain closed-loop maps: a classical result is the Youla parameterization, and two recent notions are the system-level parameterization (SLP) and the input-output parameterization (IOP). In this paper, we address the existence of new convex parameterizations and discuss potential tradeoffs of each parametrization in different scenarios. Our main contributions are: 1) We reveal that only four groups of stable closed-loop transfer matrices are equivalent to internal stability: one of them is used in the SLP, another one is used in the IOP, and the other two are new, leading to two new convex parameterizations of $\mathcal{C}_{\text{stab}}$. 2) We investigate the properties of these parameterizations after imposing the finite impulse response (FIR) approximation, revealing that the IOP has the best ability of approximating $\mathcal{C}_{\text{stab}}$ given FIR constraints. 3) These four parameterizations require no \emph{a priori} doubly-coprime factorization of the plant, but impose a set of equality constraints. However, these equality constraints will never be satisfied exactly in floating-point arithmetic computation and/or implementation. We prove that the IOP is numerically robust for open-loop stable plants, in the sense that small mismatches in the equality constraints do not compromise the closed-loop stability; but a direct IOP implementation will fail to stabilize open-loop unstable systems in practice. The SLP is known to enjoy numerical robustness in the state feedback case; here, we show that numerical robustness of the four-block SLP controller requires case-by-case analysis even the plant is open-loop stable.

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preprint2021arXiv

Performance guarantees of forward and reverse greedy algorithms for minimizing nonsupermodular nonsubmodular functions on a matroid

This letter studies the problem of minimizing increasing set functions, or equivalently, maximizing decreasing set functions, over the base of a matroid. This setting has received great interest, since it generalizes several applied problems including actuator and sensor placement problems in control theory, multi-robot task allocation problems, video summarization, and many others. We study two greedy heuristics, namely, the forward and the reverse greedy algorithms. We provide two novel performance guarantees for the approximate solutions obtained by these heuristics depending on both the submodularity ratio and the curvature.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Safe non-smooth black-box optimization with application to policy search

For safety-critical black-box optimization tasks, observations of the constraints and the objective are often noisy and available only for the feasible points. We propose an approach based on log barriers to find a local solution of a non-convex non-smooth black-box optimization problem $\min f^0(x)$ subject to $f^i(x)\leq 0,~ i = 1,\ldots, m$, at the same time, guaranteeing constraint satisfaction while learning an optimal solution with high probability. Our proposed algorithm exploits noisy observations to iteratively improve on an initial safe point until convergence. We derive the convergence rate and prove safety of our algorithm. We demonstrate its performance in an application to an iterative control design problem.

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preprint2021arXiv

Using Uncertainty Data in Chance-Constrained Trajectory Planning

We consider the problem of trajectory planning in an environment comprised of a set of obstacles with uncertain locations. While previous approaches model the uncertainties with a prescribed Gaussian distribution, we consider the realistic case in which the distribution's moments are unknown and are learned online. We derive tight concentration bounds on the error of the estimated moments. These bounds are then used to derive a tractable and tight mixed-integer convex reformulation of the trajectory planning problem, assuming linear dynamics and polyhedral constraints. The solution of the resulting optimization program is a feasible solution for the original problem with high confidence. We illustrate the approach with a case study from autonomous driving.

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preprint2020arXiv

An Input-Output Parametrization of Stabilizing Controllers: amidst Youla and System Level Synthesis

This paper proposes a novel input-output parametrization of the set of internally stabilizing output-feedback controllers for linear time-invariant (LTI) systems. Our underlying idea is to directly treat the closed-loop transfer matrices from disturbances to input and output signals as design parameters and exploit their affine relationships. This input-output perspective is particularly effective when a doubly-coprime factorization is difficult to compute, or an initial stabilizing controller is challenging to find; most previous work requires one of these pre-computation steps. Instead, our approach can bypass such pre-computations, in the sense that a stabilizing controller is computed by directly solving a linear program (LP). Furthermore, we show that the proposed input-output parametrization allows for computing norm-optimal controllers subject to quadratically invariant (QI) constraints using convex programming.

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preprint2020arXiv

Learning to Play Sequential Games versus Unknown Opponents

We consider a repeated sequential game between a learner, who plays first, and an opponent who responds to the chosen action. We seek to design strategies for the learner to successfully interact with the opponent. While most previous approaches consider known opponent models, we focus on the setting in which the opponent's model is unknown. To this end, we use kernel-based regularity assumptions to capture and exploit the structure in the opponent's response. We propose a novel algorithm for the learner when playing against an adversarial sequence of opponents. The algorithm combines ideas from bilevel optimization and online learning to effectively balance between exploration (learning about the opponent's model) and exploitation (selecting highly rewarding actions for the learner). Our results include algorithm's regret guarantees that depend on the regularity of the opponent's response and scale sublinearly with the number of game rounds. Moreover, we specialize our approach to repeated Stackelberg games, and empirically demonstrate its effectiveness in a traffic routing and wildlife conservation task

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preprint2020arXiv

Minimizing Regret of Bandit Online Optimization in Unconstrained Action Spaces

We consider online convex optimization with a zero-order oracle feedback. In particular, the decision maker does not know the explicit representation of the time-varying cost functions, or their gradients. At each time step, she observes the value of the corresponding cost function evaluated at her chosen action (zero-order oracle). The objective is to minimize the regret, that is, the difference between the sum of the costs she accumulates and that of a static optimal action had she known the sequence of cost functions a priori. We present a novel algorithm to minimize regret in unconstrained action spaces. Our algorithm hinges on a classical idea of one-point estimation of the gradients of the cost functions based on their observed values. The algorithm is independent of problem parameters. Letting $T$ denote the number of queries of the zero-order oracle and $n$ the problem dimension, the regret rate achieved is $O(n^{2/3}T^{2/3})$. Moreover, we adapt the presented algorithm to the setting with two-point feedback and demonstrate that the adapted procedure achieves the theoretical lower bound on the regret of $(n^{1/2}T^{1/2})$.

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preprint2020arXiv

Mixed Strategies for Robust Optimization of Unknown Objectives

We consider robust optimization problems, where the goal is to optimize an unknown objective function against the worst-case realization of an uncertain parameter. For this setting, we design a novel sample-efficient algorithm GP-MRO, which sequentially learns about the unknown objective from noisy point evaluations. GP-MRO seeks to discover a robust and randomized mixed strategy, that maximizes the worst-case expected objective value. To achieve this, it combines techniques from online learning with nonparametric confidence bounds from Gaussian processes. Our theoretical results characterize the number of samples required by GP-MRO to discover a robust near-optimal mixed strategy for different GP kernels of interest. We experimentally demonstrate the performance of our algorithm on synthetic datasets and on human-assisted trajectory planning tasks for autonomous vehicles. In our simulations, we show that robust deterministic strategies can be overly conservative, while the mixed strategies found by GP-MRO significantly improve the overall performance.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Safe Mission Planning under Dynamical Uncertainties

This paper considers safe robot mission planning in uncertain dynamical environments. This problem arises in applications such as surveillance, emergency rescue, and autonomous driving. It is a challenging problem due to modeling and integrating dynamical uncertainties into a safe planning framework, and finding a solution in a computationally tractable way. In this work, we first develop a probabilistic model for dynamical uncertainties. Then, we provide a framework to generate a path that maximizes safety for complex missions by incorporating the uncertainty model. We also devise a Monte Carlo method to obtain a safe path efficiently. Finally, we evaluate the performance of our approach and compare it to potential alternatives in several case studies.

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preprint2020arXiv

Sparsity Invariance for Convex Design of Distributed Controllers

We address the problem of designing optimal linear time-invariant (LTI) sparse controllers for LTI systems, which corresponds to minimizing a norm of the closed-loop system subject to sparsity constraints on the controller structure. This problem is NP-hard in general and motivates the development of tractable approximations. We characterize a class of convex restrictions based on a new notion of Sparsity Invariance (SI). The underlying idea of SI is to design sparsity patterns for transfer matrices Y(s) and X(s) such that any corresponding controller K(s)=Y(s)X(s)^-1 exhibits the desired sparsity pattern. For sparsity constraints, the approach of SI goes beyond the notion of Quadratic Invariance (QI): 1) the SI approach always yields a convex restriction; 2) the solution via the SI approach is guaranteed to be globally optimal when QI holds and performs at least as well as considering a nearest QI subset. Moreover, the notion of SI naturally applies to designing structured static controllers, while QI is not utilizable. Numerical examples show that even for non-QI cases, SI can recover solutions that are 1) globally optimal and 2) strictly more performing than previous methods.

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preprint2019arXiv

Distributed Design for Decentralized Control using Chordal Decomposition and ADMM

We propose a distributed design method for decentralized control by exploiting the underlying sparsity properties of the problem. Our method is based on chordal decomposition of sparse block matrices and the alternating direction method of multipliers (ADMM). We first apply a classical parameterization technique to restrict the optimal decentralized control into a convex problem that inherits the sparsity pattern of the original problem. The parameterization relies on a notion of strongly decentralized stabilization, and sufficient conditions are discussed to guarantee this notion. Then, chordal decomposition allows us to decompose the convex restriction into a problem with partially coupled constraints, and the framework of ADMM enables us to solve the decomposed problem in a distributed fashion. Consequently, the subsystems only need to share their model data with their direct neighbours, not needing a central computation. Numerical experiments demonstrate the effectiveness of the proposed method.

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preprint2019arXiv

On the Equivalence of Youla, System-level and Input-output Parameterizations

A convex parameterization of internally stabilizing controllers is fundamental for many controller synthesis procedures. The celebrated Youla parameterization relies on a doubly-coprime factorization of the system, while the recent system-level and input-output characterizations require no doubly-coprime factorization but a set of equality constraints for achievable closed-loop responses. In this paper, we present explicit affine mappings among Youla, system-level and input-output parameterizations. Two direct implications of the affine mappings are 1) any convex problem in Youla, system level, or input-output parameters can be equivalently and convexly formulated in any other one of these frameworks, including the convex system-level synthesis (SLS); 2) the condition of quadratic invariance (QI) is sufficient and necessary for the classical distributed control problem to admit an equivalent convex reformulation in terms of Youla, system-level, or input-output parameters.

0 citations0 reviewsNo code linkedOpen access
preprint2018arXiv

Exploiting structure of chance constrained programs via submodularity

We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the computational cost of the scenario program. We exploit the problem structure by efficiently partitioning the constraint function and considering a multiple chance constrained program that gives the same probabilistic guarantees as the original single chance constrained problem. We formulate the problem of finding the optimal partition, a partition achieving the lowest computational cost, as an optimization problem with nonlinear objective and combinatorial constraints. By using submodularity of the support rank of a set of constraints, we propose a polynomial-time algorithm to find suboptimal solutions to this partitioning problem and we give approximation guarantees for special classes of cost metrics. We illustrate that the resulting computational cost savings can be arbitrarily large and demonstrate our approach on two case studies from production and multi-agent planning.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Exploring Vickrey-Clarke-Groves Mechanism for Electricity Markets

Control reserves are power generation or consumption entities that ensure balance of supply and demand of electricity in real-time. In many countries, they are operated through a market mechanism in which entities provide bids. The system operator determines the accepted bids based on an optimization algorithm. We develop the Vickrey-Clarke-Groves (VCG) mechanism for these electricity markets. We show that all advantages of the VCG mechanism including incentive compatibility of the equilibria and efficiency of the outcome can be guaranteed in these markets. Furthermore, we derive conditions to ensure collusion and shill bidding are not profitable. Our results are verified with numerical examples.

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preprint2016arXiv

Payoff-Based Approach to Learning Nash Equilibria in Convex Games

We consider multi-agent decision making, where each agent optimizes its cost function subject to constraints. Agents' actions belong to a compact convex Euclidean space and the agents' cost functions are coupled. We propose a distributed payoff-based algorithm to learn Nash equilibria in the game between agents. Each agent uses only information about its current cost value to compute its next action. We prove convergence of the proposed algorithm to a Nash equilibrium in the game leveraging established results on stochastic processes. The performance of the algorithm is analyzed with a numerical case study.

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preprint2016arXiv

Robust Optimal Control with Adjustable Uncertainty Sets

In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional decision variables. In particular, given a finite prediction horizon and a metric for adjusting the uncertainty sets, we address the question of determining the optimal size and shape of the uncertainty sets, while simultaneously ensuring the existence of a control policy that will keep the system within its constraints for all possible disturbance realizations inside the adjusted uncertainty set. Since our problem subsumes the classical constrained robust optimal control design problem, it is computationally intractable in general. We demonstrate that by restricting the families of admissible uncertainty sets and control policies, the problem can be formulated as a tractable convex optimization problem. We show that our framework captures several families of (convex) uncertainty sets of practical interest, and illustrate our approach on a demand response problem of providing control reserves for a power system.

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preprint2015arXiv

Upper bounds for the reach-avoid probability via robust optimization

We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by restricting attention to the span of Gaussian radial basis functions and imposing structural assumptions on the transition kernel of the stochastic processes as well as the target and safe sets of the reach-avoid problem. In particular, we require the kernel to be written as a Gaussian mixture density with each mean of the distribution being affine in the current state and input and the target and safe sets to be written as intersections of quadratic inequalities. Taking advantage of these structural assumptions, we formulate a recursion of semidefinite programs where each step provides an upper bound to the value function of the reach- avoid problem. The upper bounds provide a performance metric to which any suboptimal control policy can be compared, and can themselves be used to construct suboptimal control policies. We illustrate via numerical examples that even if the resulting bounds are conservative, the associated control policies achieve higher reach-avoid probabilities than heuristic controllers for problems of large state-input space dimensions (more than 20). The results presented in this paper, far exceed the limits of current approximation methods for reach-avoid problems in the specific class of stochastic systems considered.

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preprint2012arXiv

Approximate Dynamic Programming via Sum of Squares Programming

We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision variables. By relaxing the Bellman equation to an inequality, one obtains a linear program in the basis coefficients with an infinite set of constraints. We show that a recently introduced method, which obtains convex quadratic value function approximations, can be extended to higher order polynomial approximations via sum of squares programming techniques. An approximate value function can then be computed offline by solving a semidefinite program, without having to sample the infinite constraint. The policy is evaluated online by solving a polynomial optimization problem, which also turns out to be convex in some cases. We experimentally validate the method on an autonomous helicopter testbed using a 10-dimensional helicopter model.

0 citations0 reviewsNo code linkedOpen access