Sina Sharifi

Jiarui Wang, Sina Sharifi, Mahyar Fazlyab

Model Predictive Path Integral (MPPI) control is a powerful sampling-based method for solving stochastic optimal control problems and has enabled real-time control in complex robotic systems. Despite its empirical success, its theoretical understanding remains limited. In this work, we show that MPPI can be interpreted as a special case of the Expectation-Maximization (EM) algorithm applied to a probabilistic inference formulation of optimal control. This perspective leads to a generalized EM-MPPI framework that extends MPPI beyond the commonly used Gaussian parameterization. We analyze the convergence behavior of this algorithm and characterize the local convergence rate in terms of the covariance of the posterior trajectory distribution and the exploration distribution. For exponential-family distributions, we establish a sufficient increase property of the log-likelihood when the log-partition function is strongly convex. Specializing the analysis to Gaussian MPPI yields explicit global and local convergence characterizations. The code for the experiments will be available upon acceptance.

Mahyar Fazlyab, Sina Sharifi, Jiarui Wang

Model Predictive Path Integral (MPPI) control is a popular sampling-based method for trajectory optimization in nonlinear and nonconvex settings, yet its optimization structure remains only partially understood. We develop a variational, optimization-theoretic interpretation of MPPI by lifting constrained trajectory optimization to a KL-regularized problem over distributions and reducing it to a negative log-partition (free-energy) objective over a tractable sampling family. For a general parametric family, this yields a preconditioned gradient method on the distribution parameters and a natural multi-step extension of MPPI. For the fixed-covariance Gaussian family, we show that classical MPPI is recovered exactly as a preconditioned gradient descent step with unit step size. This interpretation enables a direct convergence analysis: under bounded feasible sets, we derive an explicit upper bound on the smoothness constant and a simple sufficient condition guaranteeing descent of exact MPPI. Numerical experiments support the theory and illustrate the effect of key hyperparameters on performance.

Sina Sharifi, Taha Entesari, Bardia Safaei et al.

One of the challenges for neural networks in real-life applications is the overconfident errors these models make when the data is not from the original training distribution. Addressing this issue is known as Out-of-Distribution (OOD) detection. Many state-of-the-art OOD methods employ an auxiliary dataset as a surrogate for OOD data during training to achieve improved performance. However, these methods fail to fully exploit the local information embedded in the auxiliary dataset. In this work, we propose the idea of leveraging the information embedded in the gradient of the loss function during training to enable the network to not only learn a desired OOD score for each sample but also to exhibit similar behavior in a local neighborhood around each sample. We also develop a novel energy-based sampling method to allow the network to be exposed to more informative OOD samples during the training phase. This is especially important when the auxiliary dataset is large. We demonstrate the effectiveness of our method through extensive experiments on several OOD benchmarks, improving the existing state-of-the-art FPR95 by 4% on our ImageNet experiment. We further provide a theoretical analysis through the lens of certified robustness and Lipschitz analysis to showcase the theoretical foundation of our work. Our code is available at https://github.com/o4lc/Greg-OOD.

Sina Sharifi, Nazanin Abolfazli, Erfan Yazdandoost Hamedani et al.

Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our method consists of two components: a gradient flow mechanism to minimize the upper-level objective and a safety filter to enforce the constraints imposed by the lower-level problem. Together, these components form a safe gradient flow that solves the bilevel problem in a single loop. To improve scalability with respect to the lower-level problem's dimensions, we introduce a relaxed formulation and design a compact variant of the safe gradient flow. This variant minimizes the upper-level objective while ensuring the lower-level decision variable remains within a user-defined suboptimality. Using Lyapunov analysis, we establish convergence guarantees for the dynamics, proving that they converge to a neighborhood of the optimal solution. Numerical experiments further validate the effectiveness of the proposed approaches. Our contributions provide both theoretical insights and practical tools for efficiently solving bilevel optimization problems.

Sina Sharifi, Erfan Yazdandoost Hamedani, Mahyar Fazlyab

Bilevel optimization involves a hierarchical structure where one problem is nested within another, leading to complex interdependencies between levels. We propose a single-loop, tuning-free algorithm that guarantees anytime feasibility, i.e., approximate satisfaction of the lower-level optimality condition, while ensuring descent of the upper-level objective. At each iteration, a convex quadratically-constrained quadratic program (QCQP) with a closed-form solution yields the search direction, followed by a backtracking line search inspired by control barrier functions to ensure safe, uniformly positive step sizes. The resulting method is scalable, requires no hyperparameter tuning, and converges under mild local regularity assumptions. We establish an O(1/k) ergodic convergence rate in terms of a first-order stationary metric and demonstrate the algorithm's effectiveness on representative bilevel tasks.

Taha Entesari, Sina Sharifi, Mahyar Fazlyab

A key challenge that threatens the widespread use of neural networks in safety-critical applications is their vulnerability to adversarial attacks. In this paper, we study the second-order behavior of continuously differentiable deep neural networks, focusing on robustness against adversarial perturbations. First, we provide a theoretical analysis of robustness and attack certificates for deep classifiers by leveraging local gradients and upper bounds on the second derivative (curvature constant). Next, we introduce a novel algorithm to analytically compute provable upper bounds on the second derivative of neural networks. This algorithm leverages the compositional structure of the model to propagate the curvature bound layer-by-layer, giving rise to a scalable and modular approach. The proposed bound can serve as a differentiable regularizer to control the curvature of neural networks during training, thereby enhancing robustness. Finally, we demonstrate the efficacy of our method on classification tasks using the MNIST and CIFAR-10 datasets.

Sina Sharifi, Mahyar Fazlyab

We propose a novel reachability analysis method tailored for neural networks with differentiable activations. Our idea hinges on a sound abstraction of the neural network map based on first-order Taylor expansion and bounding the remainder. To this end, we propose a method to compute analytical bounds on the network's first derivative (gradient) and second derivative (Hessian). A key aspect of our method is loop transformation on the activation functions to exploit their monotonicity effectively. The resulting end-to-end abstraction locally preserves the derivative information, yielding accurate bounds on small input sets. Finally, we employ a branch and bound framework for larger input sets to refine the abstraction recursively. We evaluate our method numerically via different examples and compare the results with relevant state-of-the-art methods.