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Peyman Mohajerin Esfahani

Publications and source records attributed to Peyman Mohajerin Esfahani.

At least 19 recordsLinked to original sources
arXiv2026

Limiting-Kernel Q($λ$): Bridging Short and Long Horizons

In reinforcement learning, more accurate policy evaluation has been frequently shown to improve downstream policy optimization performance. For tractability, most value estimators rely on $n$-step truncation and thereby omit the long-horizon behavior of the transition dynamics. Methods that instead capture this behavior through the global structure of the dynamics can converge faster, but their computational and memory requirements limit their scalability to large or continuous state spaces. To reconcile these limitations, we introduce Limiting-Kernel Q($λ$) (LKQL), an off-policy value estimator that uses the limiting kernel to approximate the long-horizon terms omitted by truncation. LKQL has the same order of complexity as $n$-step estimators and integrates directly into both on- and off-policy actor-critic algorithms. We prove that, under aperiodicity and in the near-on-policy regime, the operator underlying LKQL improves the policy evaluation convergence rate over its truncated counterpart for sufficiently large $n$, and that LKQL itself converges almost surely to the optimal values in finite Markov decision processes (MDPs) under a fixed behavior policy. On the MuJoCo continuous-control benchmark, we show that LKQL improves over $n$-step baselines in most settings, particularly on long-horizon tasks.

cs.LG↗
arXiv2026

Accelerating Adaptive Systems via Normalized Parameter Estimation Laws

In this paper, we propose a new class of parameter estimation laws for adaptive systems, called \emph{normalized parameter estimation laws}. A key feature of these estimation laws is that they accelerate the convergence of the system state, $\mathit{x(t)}$, to the origin. We quantify this improvement by showing that our estimation laws guarantee finite integrability of the $\mathit{r}$-th root of the squared norm of the system state, i.e., \( \mathit{\|x(t)\|}_2^{2/\mathit{r}} \in \mathcal{L}_1, \) where $\mathit{r} \geq 1$ is a pre-specified parameter that, for a broad class of systems, can be chosen arbitrarily large. In contrast, standard Lyapunov-based estimation laws only guarantee integrability of $\mathit{\|x(t)\|}_2^2$ (i.e., $\mathit{r} = 1$). We motivate our method by showing that, for large values of $r$, this guarantee serves as a sparsity-promoting mechanism in the time domain, meaning that it penalizes prolonged signal duration and slow decay, thereby promoting faster convergence of $\mathit{x(t)}$. The proposed estimation laws do not rely on time-varying or high adaptation gains and do not require persistent excitation. Moreover, they can be applied to systems with matched and unmatched uncertainties, regardless of their dynamic structure, as long as a control Lyapunov function (CLF) exists. Finally, they are compatible with any CLF-based certainty equivalence controllers. We further develop higher-order extensions of our estimation laws by incorporating momentum into the estimation dynamics. We illustrate the performance improvements achieved with the proposed scheme through various numerical experiments.

eess.SY↗
arXiv2026

Learning in Inverse Games: Tractable Training with Probabilistic Guarantees

Inverse game theory seeks to learn agents' unknown objectives from observed equilibrium behavior. Existing residual-based approaches can lead to non-convex problems and need not ensure strong monotonicity of the learned game, limiting reliable equilibrium prediction. We develop a tractable convex framework for learning static and dynamic non-cooperative games using first-order and Nikaido-Isoda (NI) loss. Specialized operator parameterizations, including a Helmholtz--Hodge decomposition in a reproducing kernel Hilbert space (RKHS), enforce strong monotonicity for quadratic, nonparametric, non-quadratic, and linear-quadratic dynamic games. We establish finite-sample out-of-sample prediction guarantees, using Rademacher complexity to match existing bounds for the non-quadratic setting. For noisy sequential data, we develop a robust receding-horizon learning scheme whose adaptive regularization admits a maximum a posteriori (MAP) interpretation and is computed using randomized trace estimation. Numerical experiments, including a stylized autonomous-vehicle collision-avoidance application, demonstrate predictive accuracy and robustness to measurement noise.

eess.SY↗
arXiv2026

Benign Geometry and Distributional Robustness of $\mathcal{H}_2$ Synthesis

In this paper, we study standard and distributionally robust $\mathcal{H}_2$ synthesis problem of a stabilizing state-feedback controller for discrete-time linear time-invariant systems. Without requiring a nonsingular disturbance controllability Gramian or a positive-definite control penalty, we establish that stationarity of a stabilizing gain in standard $\mathcal{H}_2$ synthesis is equivalent to global optimality and derive an exact Pythagorean identity for the performance difference. We then generalize the $\mathcal{H}_2$ synthesis problem by considering i.i.d. disturbances with zero mean and uniformly bounded second moments, and extend the stationarity-optimality equivalence to the corresponding distributionally robust $\mathcal{H}_2$ synthesis. Moreover, we show that every standard $\mathcal{H}_2$-optimal gain is simultaneously optimal for every such distributionally robust problem. Finally, we specialize the framework to Frobenius, Kullback--Leibler, and Wasserstein-2 ambiguity sets and obtain explicit characterizations of their worst-case covariances, which, in turn, provide performance certificates for a common optimal controller.

math.OC↗
arXiv2026

A New Lineserach for Accelerated Composite Minimization

The choice of the stepsize in first-order convex optimization is typically based on the smoothness constant and plays a crucial role in the performance of algorithms. Recently, there has been a resurgent interest in introducing adaptive stepsizes that do not explicitly depend on smooth constant. In this paper, we propose a novel linesearch stepsize rule based on function evaluations (i.e., zero-order information) that enjoys provable convergence guarantees for both accelerated and non-accelerated gradient descent. We further discuss the similarities and differences between the proposed stepsize regimes and the existing stepsize rules (including Polyak and Armijo). We numerically benchmark the performance of our proposed algorithms against state-of-the-art methods across three major problems classes of (1) smooth minimization (logistic regression, quadratic programs, log-sum-exponential, and smooth max-cut relaxation) (2) composite minimization ($\ell_1$-regularized least-squares, $\ell_1$-constrained least-squares, and $\ell_1$-regularized logistic regression), and (3) non-convex minimization (cubic minimization). These classes include a wide range of operations research and management applications such as portfolio optimization, discrete choice models, sparse classification and feature selections, high-order optimization and trust-region subproblems.

math.OC↗
arXiv2026

Adaptive Incentive Design in Dynamic Principal-Agent Problem via Kernelized Bandits

We consider the dynamic principal-agent problem under asymmetric information, wherein a principal sequentially designs contracts to incentivize an agent with unknown preferences and hidden actions. A fundamental bottleneck in the existing literature is the assumption of deterministic agent utility, which renders the principal's expected utility discontinuous and forces computationally intractable discretizations of the contract space. In this paper, we address this limitation by introducing a stochastic counterpart into the agent's utility model, capturing the inherent physical and behavioral variations in realistic subsystems. We formally prove that this stochastic formulation restores the continuity of the principal's expected utility. Leveraging this continuous geometric structure, we formulate the interaction as a structured multi-armed bandit problem subject to heteroscedastic noise. We propose a \texttt{Heteroscedastic GP-UCB} algorithm that utilizes a Neural Network (Arcsin) kernel, chosen to capture the non-stationary, sigmoidal geometry of the utility landscape. For an $m$-dimensional compact contract space, we establish a high-probability cumulative regret bound of $O\left(\sqrt{T}(\log T)^{m+1}\right)$. Finally, we demonstrate the practical efficacy of our theoretical framework by formulating the Vehicle-to-Grid (V2G) incentive design problem, proving its equivalence to a dynamic principal-agent problem, and showing superior economic performance for grid aggregators.

cs.MA↗
arXiv2026

Discrete-Time Adaptive Control in High Dimensions: Near Dimension-Free Performance via Mirror Descent

Motivated by the use of modern high-capacity models in real-time control problems, this paper studies the adaptive control of high-dimensional discrete-time nonlinear systems with an unknown matrix-valued parameter. We focus on regimes where the number of unknown parameter entries is large, but the parameter matrix possesses exploitable structure, such as entrywise sparsity, group sparsity, low rank, and row-stochastic or density-matrix structure. To quantify transient performance, we consider a regret criterion relative to a nominal controller with full knowledge of the true parameter. We show that standard Euclidean update schemes, including recursive least squares and gradient descent, are ill-suited to this setting: their transient performance deteriorates as the dimension increases, even when the true parameter has low intrinsic complexity. To address this limitation, we propose a novel class of mirror-descent-type adaptive laws equipped with a non-Euclidean Polyak-type step size that exploit the geometry induced by the parameter structure. For the proposed update laws, we establish asymptotic state convergence and derive regret bounds with at most logarithmic dependence on the ambient dimension. Numerical experiments demonstrate the effectiveness of the proposed schemes.

math.OC↗
arXiv2026

Nonlinear Bayesian Estimator for Parameter Learning: A Fixed-Point Characterization

This paper presents a nonlinear parameter estimator for Wiener-type state-space models obtained as a fixed-point architecture that couples two affine minimum mean-squared error (MMSE) estimators: one for the unknown parameters and one for latent variables. The architecture retains the functional structure of the optimal affine MMSE parameter estimator while incorporating Dynamic Basis Statistics (DBS) estimates that summarize nonlinear basis-function evaluations. Two DBS construction strategies are developed, leading to two nonlinear estimator frameworks. The dual basis-parameter estimator combines an affine basis estimator with the affine parameter estimator, whereas the dual state-parameter estimator first computes affine state estimates and their covariances, then maps these state-estimate statistics through a Gaussian DBS operator to obtain DBS estimates. Both dual estimators admit fixed-point characterizations that alternate between estimating each component using the updated prior of the other, obtained from that component's plug-in estimate statistics from the previous iteration. The efficacy of the proposed methods is examined via extensive Monte Carlo experiments, showing that the dual basis-parameter estimator attains parameter mean-squared errors comparable to those of the purely affine parameter estimator, while the dual state-parameter estimator achieves the lowest parameter mean-squared error, outperforming both the dual basis-parameter and purely affine parameter estimators, as well as sequential Monte Carlo variants of classical Particle Gibbs and Expectation-Maximization schemes.

cs.LG↗
arXiv2026

Tight Generalization Bounds for Noiseless Inverse Optimization

Inverse optimization (IO) seeks to infer the parameters of a decision-maker's objective from observed context--action data. We study noiseless IO, where demonstrations are generated by a ground-truth objective. We provide a high-probability ${O}(\frac{d}{T})$ generalization bound for the induced action set, where $d$ is the number of unknown parameters and $T$ is the size of the training dataset. We strengthen these guarantees under additional conditions that ensure uniqueness of the chosen action, bringing our IO guarantees in line with best-arm identification results in the bandit literature. We further show that the ${O}(\frac{d}{T})$ rate is tight over all consistent estimators considered here, and extend the result to both instantaneous and cumulative regret. Notably, the resulting regret lower bound matches the corresponding upper bounds in the adversarial setting, indicating that the stochastic IO setting is effectively adversarial for the class of estimators studied here. Finally, we propose a parameter-free algorithm with lower per-iteration complexity than generic solvers. Experiments validate the predicted rates and illustrate the tightness of our bounds.

stat.ML↗
arXiv2026

Locally Linear Convergence for Nonsmooth Convex Optimization via Coupled Smoothing and Momentum

We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function is the sum of two nonsmooth functions. With regard to convergence rate, we provide the global (optimal) sublinear convergence guarantees of O(1/k), which is known to be provably optimal for the studied class of functions, along with a local linear rate if the nonsmooth term fulfills a so-call locally strong convexity condition. We validate the performance of our algorithm on several problem classes, including regression with the l1-norm (the Lasso problem), sparse semidefinite programming (the MaxCut problem), Nuclear norm minimization with application in model free fault diagnosis, and l_1-regularized model predictive control to showcase the benefits of the coupling. An interesting observation is that although our global convergence result guarantees O(1/k) convergence, we consistently observe a practical transient convergence rate of O(1/k^2), followed by asymptotic linear convergence as anticipated by the theoretical result. This two-phase behavior can also be explained in view of the proposed smoothing rule.

math.OC↗
arXiv2026

A Saddle Point Algorithm for Robust Data-Driven Factor Model Problems

We study the factor model problem, which aims to uncover low-dimensional structures in high-dimensional datasets. Adopting a robust data-driven approach, we formulate the problem as a saddle-point optimization. Our primary contribution is a first-order algorithm that solves this reformulation by leveraging a linear minimization oracle (LMO). We further develop semi-closed form solutions (up to a scalar) for three specific LMOs, corresponding to the Frobenius norm, Kullback-Leibler divergence, and Gelbrich (aka Wasserstein) distance. The analysis includes explicit quantification of these LMOs' regularity conditions, notably the Lipschitz constants of the dual function, which govern the algorithm's convergence performance. Numerical experiments confirm our method's effectiveness in high-dimensional settings, outperforming standard off-the-shelf optimization solvers.

math.OC↗
arXiv2026

A Hybrid Algorithm for Monotone Variational Inequalities

Inspired by the adaptive Golden Ratio Algorithm (aGRAAL), we propose two new methods for solving monotone variational inequalities. We show that by selecting the momentum parameter beyond the golden ratio in aGRAAL, the convergence speed can be improved, which motivates us to study the switching between small and large momentum parameters to accelerate convergence. We validate the performance of our proposed algorithms on several classes of variational inequality problems studied in the machine learning and control literature, including Nash equilibrium seeking, composite minimization, Markov decision processes, and zero-sum games, and compare them to that of existing methods.

math.OC↗
arXiv2026

Offline Reinforcement Learning via Inverse Optimization

Inspired by the recent successes of Inverse Optimization (IO) across various application domains, we propose a novel offline Reinforcement Learning (ORL) algorithm for continuous state and action spaces, leveraging the convex loss function called ``sub-optimality loss'' from the IO literature. To mitigate the distribution shift commonly observed in ORL problems, we further employ a robust and non-causal Model Predictive Control (MPC) expert steering a nominal model of the dynamics using in-hindsight information stemming from the model mismatch. Unlike the existing literature, our robust MPC expert enjoys an exact and tractable convex reformulation. In the second part of this study, we show that the IO hypothesis class, trained by the proposed convex loss function, enjoys ample expressiveness and {reliably recovers teacher behavior in MuJoCo benchmarks. The method achieves competitive results compared to widely-used baselines in sample-constrained settings, despite using} orders of magnitude fewer parameters. To facilitate the reproducibility of our results, we provide an open-source package implementing the proposed algorithms and the experiments. The code is available at https://github.com/TolgaOk/offlineRLviaIO.

cs.LG↗
arXiv2026

Rate or Fate? RLV$^\varepsilon$R: Reinforcement Learning with Verifiable Noisy Rewards

Reinforcement learning with verifiable rewards (RLVR) is a simple but powerful paradigm for training LLMs: sample a completion, verify it, and update. In practice, however, the verifier is almost never clean--unit tests probe only limited corner cases; human and synthetic labels are imperfect; and LLM judges (e.g., RLAIF) are noisy and can be exploited--and this problem worsens on harder domains (especially coding) where tests are sparse and increasingly model-generated. We ask a pragmatic question: does the verification noise merely slow down the learning (rate), or can it flip the outcome (fate)? To address this, we develop an analytically tractable multi-armed bandit view of RLVR dynamics, instantiated with GRPO and validated in controlled experiments. Modeling false positives and false negatives and grouping completions into recurring reasoning modes yields a replicator-style (natural-selection) flow on the probability simplex. The dynamics decouples into within-correct-mode competition and a one-dimensional evolution for the mass on incorrect modes, whose drift is determined solely by Youden's index J=TPR-FPR. This yields a sharp phase transition: when J>0, the incorrect mass is driven toward extinction (learning); when J=0, the process is neutral; and when J<0, incorrect modes amplify until they dominate (anti-learning and collapse). In the learning regime J>0, noise primarily rescales convergence time ("rate, not fate"). Experiments on verifiable programming tasks under synthetic noise reproduce the predicted J=0 boundary. Beyond noise, the framework offers a general lens for analyzing RLVR stability, convergence, and algorithmic interventions.

cs.LG↗
arXiv2026

From Optimization to Control: Quasi Policy Iteration

Recent control algorithms for Markov decision processes (MDPs) have been designed using an implicit analogy with well-established optimization algorithms. In this paper, we adopt the quasi-Newton method (QNM) from convex optimization to introduce a novel control algorithm coined as quasi-policy iteration (QPI). In particular, QPI is based on a novel approximation of the ``Hessian'' matrix in the policy iteration algorithm, which exploits two linear structural constraints specific to MDPs and allows for the incorporation of prior information on the transition probability kernel. While the proposed algorithm has the same computational complexity as value iteration, it exhibits an empirical convergence behavior similar to that of QNM with a low sensitivity to the discount factor.

math.OC↗
arXiv2025

Optimal Transportation by Orthogonal Coupling Dynamics

Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an infinite-dimensional linear programming, such a methodology limits the computational performance due to the polynomial scaling with respect to the sample size along with intensive memory requirements. We propose a novel alternative framework to address the Monge-Kantorovich problem based on a projection type gradient descent scheme. The dynamics builds on the notion of the conditional expectation, where the connection with the opinion dynamics is leveraged to devise efficient numerical schemes. We demonstrate that the resulting dynamics recovers random maps with favourable computational performance. Along with the theoretical insight, the proposed dynamics paves the way for innovative approaches to construct numerical schemes for computing optimal transport maps as well as Wasserstein distances.

math.OC↗
arXiv2025

Control and Reinforcement Learning through the Lens of Optimization: An Algorithmic Perspective

The connection between control algorithms for Markov decision processes and optimization algorithms has been implicitly and explicitly exploited since the introduction of dynamic programming algorithm by Bellman in the 1950s. Recently, this connection has attracted a lot of attention for developing new control algorithms inspired by well-established optimization algorithms. In this paper, we make this analogy explicit across four problem classes with a unified solution characterization. This novel framework, in turn, allows for a systematic transformation of algorithms from one domain to the other. In particular, we identify equivalent optimization and control algorithms that have already been pointed out in the existing literature, but mostly in a scattered way. We also discuss the issues arising in providing theoretical convergence guarantees for these new control algorithms and provide simple yet effective techniques to solve them. The provided framework and techniques then lay out a concrete methodology for developing new convergent control algorithms.

math.OC↗
arXiv2025

Rank-One Modified Value Iteration

In this paper, we provide a novel algorithm for solving planning and learning problems of Markov decision processes. The proposed algorithm follows a policy iteration-type update by using a rank-one approximation of the transition probability matrix in the policy evaluation step. This rank-one approximation is closely related to the stationary distribution of the corresponding transition probability matrix, which is approximated using the power method. We provide theoretical guarantees for the convergence of the proposed algorithm to optimal (action-)value function with the same rate and computational complexity as the value iteration algorithm in the planning problem and as the Q-learning algorithm in the learning problem. Through our extensive numerical simulations, however, we show that the proposed algorithm consistently outperforms first-order algorithms and their accelerated versions for both planning and learning problems.

math.OC↗