arXiv subjects

Erfaun Noorani

Publications and source records attributed to Erfaun Noorani.

16 recordsLinked to original sources

arXiv2026

A Time-to-Collision Barrier Function Approach to Collision Avoidance for Stochastic Systems

Collision avoidance constraints for autonomous systems are typically formulated in position or velocity space, implicitly reacting to geometric proximity. We propose an alternative paradigm based on the adversarial time-to-collision (aTTC): the minimum time in which an adversary could achieve a collision given its dynamical constraints. By defining a control barrier function (CBF) directly in the time domain, the resulting controller is inherently anticipatory. The evading agent responds not only to whether a pursuer is on a collision course, but to how quickly it could reach one. This formulation enables velocity modulation that exploits the pursuers dynamic limits as an evasive strategy, a behavior not captured by standard distance-based CBFs. Since exact aTTC computation requires integrating the full system dynamics, we employ a lightweight neural network surrogate that admits a real-time quadratic program-based control law. We validate the approach in a 2D comparative study and a 3D multi-agent pursuit-evasion scenario, where the aTTC-based CBF outperforms a higher-order distance-based baseline by more effectively buying time against superior pursuers with a significant speed advantage.

eess.SY↗

arXiv2026

A Temporal Barrier Framework for Collision Avoidance in Multi-Agent Autonomous Aerial Vehicles

Operating teams of autonomous aircraft in dynamic, uncertain, and potentially adversarial environments requires safety protocols that are reliable yet selective, and allow agents to fly in close proximity while making progress toward mission objectives. We introduce adversarial time-to-collision (aTTC), a risk metric that quantifies, for a given agent, how quickly any surrounding agent could reach it assuming adversarial intent. We embed aTTC into the control barrier function (CBF) framework, defining the barrier directly in time rather than distance or velocity. The resulting aTTC-CBF is inherently anticipatory: agents modulate their own velocity based not on whether a peer is on a collision course, but on how quickly one could reach collision given its dynamical constraints. A differentiable neural-network surrogate makes the aTTC computable in real time within a standard CBF quadratic program. Across long time-horizon simulations of 3D independent-pursuit and formation-flight scenarios, the aTTC-CBF achieves up to twice the waypoint progress at half the collision rate of a higher-order distance-based CBF baseline.

eess.SY↗

arXiv2026

Ergodicity in reinforcement learning

In reinforcement learning, we typically aim to optimize the expected value of the sum of rewards an agent collects over a trajectory. However, if the process generating these rewards is non-ergodic, the expected value, i.e., the average over infinitely many trajectories with a given policy, is uninformative for the average over a single, but infinitely long trajectory. Thus, if we care about how the individual agent performs during deployment, the expected value is not a good optimization objective. In this paper, we discuss the impact of non-ergodic reward processes on reinforcement learning agents through an instructive example, relate the notion of ergodic reward processes to more widely used notions of ergodic Markov chains, and present existing solutions that optimize long-term performance of individual trajectories under non-ergodic reward dynamics.

cs.LG↗

arXiv2025

Towards Efficient Risk-Sensitive Policy Gradient: An Iteration Complexity Analysis

Reinforcement Learning (RL) has shown exceptional performance across various applications, enabling autonomous agents to learn optimal policies through interaction with their environments. However, traditional RL frameworks often face challenges in terms of iteration efficiency and safety. Risk-sensitive policy gradient methods, which incorporate both expected return and risk measures, have been explored for their ability to yield safe policies, yet their iteration complexity remains largely underexplored. In this work, we conduct a rigorous iteration complexity analysis for the risk-sensitive policy gradient method, focusing on the REINFORCE algorithm with an exponential utility function. We establish an iteration complexity of $\mathcal{O}(ε^{-2})$ to reach an $ε$-approximate first-order stationary point (FOSP). Furthermore, we investigate whether risk-sensitive algorithms can achieve better iteration complexity compared to their risk-neutral counterparts. Our analysis indicates that risk-sensitive REINFORCE can potentially converge faster. To validate our analysis, we empirically evaluate the learning performance and convergence efficiency of the risk-neutral and risk-sensitive REINFORCE algorithms in multiple environments: CartPole, MiniGrid, and Robot Navigation. Empirical results confirm that risk-sensitive cases can converge and stabilize faster compared to their risk-neutral counterparts. More details can be found on our website https://anonymous.4open.science/w/riskrl.

cs.LG↗

arXiv2025

Distributed Risk-Sensitive Safety Filters for Uncertain Discrete-Time Systems

Ensuring safety in multi-agent systems is a significant challenge, particularly in settings where centralized coordination is impractical. In this work, we propose a novel risk-sensitive safety filter for discrete-time multi-agent systems with uncertain dynamics that leverages control barrier functions (CBFs) defined through value functions. Our approach relies on centralized risk-sensitive safety conditions based on exponential risk operators to ensure robustness against model uncertainties. We introduce a distributed formulation of the safety filter by deriving two alternative strategies: one based on worst-case anticipation and another on proximity to a known safe policy. By allowing agents to switch between strategies, feasibility can be ensured. Through detailed numerical evaluations, we demonstrate the efficacy of our approach in maintaining safety without being overly conservative.

eess.SY↗

arXiv2025

From Abstraction to Reality: DARPA's Vision for Robust Sim-to-Real Autonomy

The DARPA Transfer from Imprecise and Abstract Models to Autonomous Technologies (TIAMAT) program aims to address rapid and robust transfer of autonomy technologies across dynamic and complex environments, goals, and platforms. Existing methods for simulation-to-reality (sim-to-real) transfer often rely on high-fidelity simulations and struggle with broad adaptation, particularly in time-sensitive scenarios. Although many approaches have shown incredible performance at specific tasks, most techniques fall short when posed with unforeseen, complex, and dynamic real-world scenarios due to the inherent limitations of simulation. In contrast to current research that aims to bridge the gap between simulation environments and the real world through increasingly sophisticated simulations and a combination of methods typically assuming a small sim-to-real gap -- such as domain randomization, domain adaptation, imitation learning, meta-learning, policy distillation, and dynamic optimization -- TIAMAT takes a different approach by instead emphasizing transfer and adaptation of the autonomy stack directly to real-world environments by utilizing a breadth of low(er)-fidelity simulations to create broadly effective sim-to-real transfers. By abstractly learning from multiple simulation environments in reference to their shared semantics, TIAMAT's approaches aim to achieve abstract-to-real transfer for effective and rapid real-world adaptation. Furthermore, this program endeavors to improve the overall autonomy pipeline by addressing the inherent challenges in translating simulated behaviors into effective real-world performance.

cs.RO↗

arXiv2025

Counterfactual Explanations for Model Ensembles Using Entropic Risk Measures

Counterfactual explanations indicate the smallest change in input that can translate to a different outcome for a machine learning model. Counterfactuals have generated immense interest in high-stakes applications such as finance, education, hiring, etc. In several use-cases, the decision-making process often relies on an ensemble of models rather than just one. Despite significant research on counterfactuals for one model, the problem of generating a single counterfactual explanation for an ensemble of models has received limited interest. Each individual model might lead to a different counterfactual, whereas trying to find a counterfactual accepted by all models might significantly increase cost (effort). We propose a novel strategy to find the counterfactual for an ensemble of models using the perspective of entropic risk measure. Entropic risk is a convex risk measure that satisfies several desirable properties. We incorporate our proposed risk measure into a novel constrained optimization to generate counterfactuals for ensembles that stay valid for several models. The main significance of our measure is that it provides a knob that allows for the generation of counterfactuals that stay valid under an adjustable fraction of the models. We also show that a limiting case of our entropic-risk-based strategy yields a counterfactual valid for all models in the ensemble (worst-case min-max approach). We study the trade-off between the cost (effort) for the counterfactual and its validity for an ensemble by varying degrees of risk aversion, as determined by our risk parameter knob. We validate our performance on real-world datasets.

cs.LG↗

arXiv2025

Reinforcement learning with non-ergodic reward increments: robustness via ergodicity transformations

Envisioned application areas for reinforcement learning (RL) include autonomous driving, precision agriculture, and finance, which all require RL agents to make decisions in the real world. A significant challenge hindering the adoption of RL methods in these domains is the non-robustness of conventional algorithms. In particular, the focus of RL is typically on the expected value of the return. The expected value is the average over the statistical ensemble of infinitely many trajectories, which can be uninformative about the performance of the average individual. For instance, when we have a heavy-tailed return distribution, the ensemble average can be dominated by rare extreme events. Consequently, optimizing the expected value can lead to policies that yield exceptionally high returns with a probability that approaches zero but almost surely result in catastrophic outcomes in single long trajectories. In this paper, we develop an algorithm that lets RL agents optimize the long-term performance of individual trajectories. The algorithm enables the agents to learn robust policies, which we show in an instructive example with a heavy-tailed return distribution and standard RL benchmarks. The key element of the algorithm is a transformation that we learn from data. This transformation turns the time series of collected returns into one for whose increments expected value and the average over a long trajectory coincide. Optimizing these increments results in robust policies.

cs.LG↗

arXiv2024

Risk-Sensitive Reinforcement Learning with Exponential Criteria

While reinforcement learning has shown experimental success in a number of applications, it is known to be sensitive to noise and perturbations in the parameters of the system, leading to high variance in the total reward amongst different episodes in slightly different environments. To introduce robustness, as well as sample efficiency, risk-sensitive reinforcement learning methods are being thoroughly studied. In this work, we provide a definition of robust reinforcement learning policies and formulate a risk-sensitive reinforcement learning problem to approximate them, by solving an optimization problem with respect to a modified objective based on exponential criteria. In particular, we study a model-free risk-sensitive variation of the widely-used Monte Carlo Policy Gradient algorithm and introduce a novel risk-sensitive online Actor-Critic algorithm based on solving a multiplicative Bellman equation using stochastic approximation updates. Analytical results suggest that the use of exponential criteria generalizes commonly used ad-hoc regularization approaches, improves sample efficiency, and introduces robustness with respect to perturbations in the model parameters and the environment. The implementation, performance, and robustness properties of the proposed methods are evaluated in simulated experiments.

eess.SY↗

arXiv2024

Robust Stochastic Shortest-Path Planning via Risk-Sensitive Incremental Sampling

With the pervasiveness of Stochastic Shortest-Path (SSP) problems in high-risk industries, such as last-mile autonomous delivery and supply chain management, robust planning algorithms are crucial for ensuring successful task completion while mitigating hazardous outcomes. Mainstream chance-constrained incremental sampling techniques for solving SSP problems tend to be overly conservative and typically do not consider the likelihood of undesirable tail events. We propose an alternative risk-aware approach inspired by the asymptotically-optimal Rapidly-Exploring Random Trees (RRT*) planning algorithm, which selects nodes along path segments with minimal Conditional Value-at-Risk (CVaR). Our motivation rests on the step-wise coherence of the CVaR risk measure and the optimal substructure of the SSP problem. Thus, optimizing with respect to the CVaR at each sampling iteration necessarily leads to an optimal path in the limit of the sample size. We validate our approach via numerical path planning experiments in a two-dimensional grid world with obstacles and stochastic path-segment lengths. Our simulation results show that incorporating risk into the tree growth process yields paths with lengths that are significantly less sensitive to variations in the noise parameter, or equivalently, paths that are more robust to environmental uncertainty. Algorithmic analyses reveal similar query time and memory space complexity to the baseline RRT* procedure, with only a marginal increase in processing time. This increase is offset by significantly lower noise sensitivity and reduced planner failure rates.

cs.AI↗

arXiv2024

Delay-Induced Watermarking for Detection of Replay Attacks in Linear Systems

A state-feedback watermarking signal design for the detection of replay attacks in linear systems is proposed. The control input is augmented with a random time-delayed term of the system state estimate, in order to secure the system against attacks of replay type. We outline the basic analysis of the closed-loop response of the state-feedback watermarking in a LQG controlled system. Our theoretical results are applied on a temperature process control example. While the proposed secure control scheme requires very involved analysis, it, nevertheless, holds promise of being superior to conventional, feed-forward, watermarking schemes, in both its ability to detect attacks as well as the secured system performance.

eess.SY↗

arXiv2024

Robust Counterfactual Explanations for Neural Networks With Probabilistic Guarantees

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the original model $m$ and the new model $M$ are bounded in the parameter space, i.e., $\|\text{Params}(M){-}\text{Params}(m)\|{<}Δ$. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed $\textit{naturally-occurring}$ model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure -- that we call $\textit{Stability}$ -- to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of $\textit{Stability}$ as defined by our measure will remain valid after potential $\textit{naturally-occurring}$ model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine practical relaxations of our proposed measure and demonstrate experimentally how they can be incorporated to find robust counterfactuals for neural networks that are close, realistic, and remain valid after potential model changes. This work also has interesting connections with model multiplicity, also known as, the Rashomon effect.

stat.ML↗

arXiv2024

Time-Robust Path Planning with Piece-Wise Linear Trajectory for Signal Temporal Logic Specifications

Real-world scenarios are characterized by timing uncertainties, e.g., delays, and disturbances. Algorithms with temporal robustness are crucial in guaranteeing the successful execution of tasks and missions in such scenarios. We study time-robust path planning for synthesizing robots' trajectories that adhere to spatial-temporal specifications expressed in Signal Temporal Logic (STL). In contrast to prior approaches that rely on {discretize}d trajectories with fixed time steps, we leverage Piece-Wise Linear (PWL) signals for the synthesis. PWL signals represent a trajectory through a sequence of time-stamped waypoints. This allows us to encode the STL formula into a Mixed-Integer Linear Program (MILP) with fewer variables. This reduction is more pronounced for specifications with a long planning horizon. To that end, we define time-robustness for PWL signals. Subsequently, we propose quantitative semantics for PWL signals according to the recursive syntax of STL and prove their soundness. We then propose an encoding strategy to transform our semantics into a MILP. Our simulations showcase the soundness and the performance of our algorithm.

eess.SY↗

arXiv2023

Risk-Sensitive Inhibitory Control for Safe Reinforcement Learning

Humans have the ability to deviate from their natural behavior when necessary, which is a cognitive process called response inhibition. Similar approaches have independently received increasing attention in recent years for ensuring the safety of control. Realized using control barrier functions or predictive safety filters, these approaches can effectively ensure the satisfaction of state constraints through an online adaptation of nominal control laws, e.g., obtained through reinforcement learning. While the focus of these realizations of inhibitory control has been on risk-neutral formulations, human studies have shown a tight link between response inhibition and risk attitude. Inspired by this insight, we propose a flexible, risk-sensitive method for inhibitory control. Our method is based on a risk-aware condition for value functions, which guarantees the satisfaction of state constraints. We propose a method for learning these value functions using common techniques from reinforcement learning and derive sufficient conditions for its success. By enforcing the derived safety conditions online using the learned value function, risk-sensitive inhibitory control is effectively achieved. The effectiveness of the developed control scheme is demonstrated in simulations.

eess.SY↗

arXiv2022

Co-Design of Watermarking and Robust Control for Security in Cyber-Physical Systems

This work discusses a novel framework for simultaneous synthesis of optimal watermarking signal and robust controllers in cyber-physical systems to minimize the loss in performance due to added watermarking signal and to maximize the detection rate of the attack. A general dynamic controller is designed to improve system performance with respect to the $\mathcal H_2$ norm, while a watermarking signal is added to improve security performance concerning the detection rate of replay attacks. The attack model considered in the paper is a replay attack, a natural attack mode when the dynamics of the system is unknown to the attacker. The paper first generalizes the existing result on the detection rate of $χ^2$ detector from a static-LQR controller to a general dynamic controller. The design improvements on both robustness and security fronts are obtained by iteratively solving the convex subsets of the formulated non-convex problem in terms of the controller and watermarking signal. A semi-definite programming optimization is formulated using Linear Matrix Inequality (LMI) results to solve the larger system-level design optimization problem. We highlight the effectiveness of our method over a simplified three-tank chemical system.

eess.SY↗

arXiv2021

Collaborative Beamforming Under Localization Errors: A Discrete Optimization Approach

We consider a network of agents that locate themselves in an environment through sensor measurements and aim to transmit a message signal to a base station via collaborative beamforming. The agents' sensor measurements result in localization errors, which degrade the quality of service at the base station due to unknown phase offsets that arise in the agents' communication channels. Assuming that each agent's localization error follows a Gaussian distribution, we study the problem of forming a reliable communication link between the agents and the base station despite the localization errors. In particular, we formulate a discrete optimization problem to choose only a subset of agents to transmit the message signal so that the variance of the signal-to-noise ratio (SNR) received by the base station is minimized while the expected SNR exceeds a desired threshold. When the variances of the localization errors are below a certain threshold characterized in terms of the carrier frequency, we show that greedy algorithms can be used to globally minimize the variance of the received SNR. On the other hand, when some agents have localization errors with large variances, we show that the variance of the received SNR can be locally minimized by exploiting the supermodularity of the mean and variance of the received SNR. In numerical simulations, we demonstrate that the proposed algorithms have the potential to synthesize beamformers orders of magnitude faster than convex optimization-based approaches while achieving comparable performances using less number of agents.

eess.SP↗