arXiv subjects

Sriram Sankaranarayanan

Publications and source records attributed to Sriram Sankaranarayanan.

At least 19 recordsLinked to original sources

arXiv2026

Optimized Piecewise Affine Abstractions of Neural Networks with Learnable Activation Functions

We present a generalized framework for the range verification of neural networks featuring non-linear activation functions. Our approach first constructs an ``optimized piecewise affine abstraction" of the network that replaces each non-linear activation function by a piecewise affine (PWA) function plus a bounded error. Such PWA functions are readily amenable to existing neural network verification techniques using specializations of linear arithmetic SMT solvers and mixed-integer optimization approaches. However, there are infinitely many ways to abstract each node, with a natural tradeoff between the number of pieces used, the global error bound, and the complexity of the resulting verification problem. We propose a dynamic programming (DP) algorithm to systematically compute the optimized PWA abstraction for general activation functions, guaranteeing tighter output bounds. The algorithm combines a local DP approximation at each node with a global error bound, yielding a variant of the knapsack problem for deciding how to allocate a fixed budget on the total number of pieces across units so as to minimize the worst-case error bound between the network and its approximation. Although the knapsack problem is itself NP-hard, we can use pseudo-polynomial DP algorithms as well as approximation schemes to solve it efficiently. Crucially, our approach is broadly applicable to diverse networks consisting of non-linear activations, including standard Multi-Layer Perceptrons (MLPs) and recently proposed architectures such as Kolmogorov-Arnold Networks (KANs). Over a series of KAN benchmarks spanning 20 to 22,000 parameters, our approach yields output bounds that are consistently of smaller width than uniform PWA allocation. The overall time taken is roughly comparable while the overhead for computing the optimized abstraction is subsumed by the time taken to compute output bounds.

cs.LG↗

arXiv2026

Learning specifications for reactive synthesis with safety constraints

This paper presents a novel approach to learning from demonstration that enables robots to autonomously execute complex tasks in dynamic environments. We model latent tasks as probabilistic formal languages and introduce a tailored reactive synthesis framework that balances robot costs with user task preferences. Our methodology focuses on safety-constrained learning and inferring formal task specifications as Probabilistic Deterministic Finite Automata (PDFA). We adapt existing evidence-driven state merging algorithms and incorporate safety requirements throughout the learning process to ensure that the learned PDFA always complies with safety constraints. Furthermore, we introduce a multi-objective reactive synthesis algorithm that generates deterministic strategies that are guaranteed to satisfy the PDFA task while optimizing the trade-offs between user preferences and robot costs, resulting in a Pareto front of optimal solutions. Our approach models the interaction as a two-player game between the robot and the environment, accounting for dynamic changes. We present a computationally-tractable value iteration algorithm to generate the Pareto front and the corresponding deterministic strategies. Comprehensive experimental results demonstrate the effectiveness of our algorithms across various robots and tasks, showing that the learned PDFA never includes unsafe behaviors and that synthesized strategies consistently achieve the task while meeting both the robot cost and user-preference requirements.

cs.RO↗

arXiv2025

Trace Repair for Temporal Behavior Trees

We present methods for repairing traces against specifications given as temporal behavior trees (TBT). TBT are a specification formalism for action sequences in robotics and cyber-physical systems, where specifications of sub-behaviors, given in signal temporal logic, are composed using operators for sequential and parallel composition, fallbacks, and repetition. Trace repairs are useful to explain failures and as training examples that avoid the observed problems. In principle, repairs can be obtained via mixed-integer linear programming (MILP), but this is far too expensive for practical applications. We present two practical repair strategies: (1) incremental repair, which reduces the MILP by splitting the trace into segments, and (2) landmark-based repair, which solves the repair problem iteratively using TBT's robust semantics as a heuristic that approximates MILP with more efficient linear programming. In our experiments, we were able to repair traces with more than 25,000 entries in under ten minutes, while MILP runs out of memory.

cs.LO↗

arXiv2025

Characterization of Safety in Stochastic Difference Inclusions using Barrier Functions

We study stochastic systems characterized by difference inclusions. Such stochastic differential inclusions are defined by set-valued maps involving the current state and stochastic input. For such systems, we investigate the problem of proving bounds on the worst-case probability of violating safety properties. Our approach uses the well-known concept of barrier functions from the study of stochastic control systems. However, barrier functions are hard to prove in the presence of stochastic inputs and adversarial choices due to the set-valued nature of the dynamics. In this paper, we show that under some assumptions on the set-valued map including upper semi-continuity and convexity combined with a concave barrier function vastly simplifies the proof of barrier conditions, allowing us to effectively substitute each random input in terms of its expectation. We prove key results based on the theory of set-valued maps and provide some interesting numerical examples. The ideas proposed here will contribute to the growing interest in problems of robust control and verification of stochastic systems in the presence of uncertain distributions and unmodeled dynamics.

math.OC↗

arXiv2025

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations

We study the problem of learning neural network models for Ordinary Differential Equations (ODEs) with parametric uncertainties. Such neural network models capture the solution to the ODE over a given set of parameters, initial conditions, and range of times. Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for learning such models that combine data-driven deep learning with symbolic physics models in a principled manner. However, the accuracy of PINNs degrade when they are used to solve an entire family of initial value problems characterized by varying parameters and initial conditions. In this paper, we combine symbolic differentiation and Taylor series methods to propose a class of higher-order models for capturing the solutions to ODEs. These models combine neural networks and symbolic terms: they use higher order Lie derivatives and a Taylor series expansion obtained symbolically, with the remainder term modeled as a neural network. The key insight is that the remainder term can itself be modeled as a solution to a first-order ODE. We show how the use of these higher order PINNs can improve accuracy using interesting, but challenging ODE benchmarks. We also show that the resulting model can be quite useful for situations such as controlling uncertain physical systems modeled as ODEs.

cs.LG↗

arXiv2025

Synthesizing Min-Max Control Barrier Functions For Switched Affine Systems

We study the problem of synthesizing non-smooth control barrier functions (CBFs) for continuous-time switched affine systems. Switched affine systems are defined by a set of affine dynamical modes, wherein the control consists of a state-based switching signal that determines the current operating mode. The control barrier functions seek to maintain the system state inside a control invariant set that excludes a given set of unsafe states. We consider CBFs that take the form of pointwise minima and maxima over a finite set of affine functions. Our approach uses ideas from nonsmooth analysis to formulate conditions for min- and max- affine control barrier functions. We show how a feedback switching law can be extracted from a given CBF. Next, we show how to automate the process of synthesizing CBFs given a system description through a tree-search algorithm inspired by branch-and-cut methods from combinatorial optimization. Finally, we demonstrate our approach on a series of interesting examples of switched affine systems.

eess.SY↗

arXiv2025

Best-response Algorithms for Lattice Convex-Quadratic Simultaneous Games

We evaluate the best-response (BR) algorithm for lattice convex-quadratic games, where the players have nonlinear objectives and unbounded feasible sets. We provide a sufficient condition that if certain interaction matrices (the product of the inverse of the positive definite matrix defining the convex-quadratic terms and the matrix that connects one player's problem to another's) have all their singular values less than 1, then the iterates do not diverge regardless of the initial point. We prove that if the iterates are trapped among finitely many strategies (called a trap), a relaxed version of the Nash equilibrium can be calculated by identifying a mixed-strategy Nash equilibrium of the finite game where the players' strategies are restricted to those in the trap. To establish the tightness of our sufficient condition, we also show examples where even if one singular value of one interaction matrix exceeds 1, there are infinitely many initial points from which the iterates diverge. Finally, we prove that if all the singular values of all the interaction matrices exceed 1, then the iterates diverge from every initial point except possibly a finite set of initializations.

cs.GT↗

arXiv2024

Proximity-based approximation algorithms for integer bilevel programs

We primarily consider bilevel programs where the lower level is a convex quadratic minimization problem under integer constraints. We show that it is $Σ_2^p$-hard to decide if the optimal objective for the leader is lesser than a given value. Following that, we consider a natural algorithm for bilevel programs that is used as a heuristic in practice. Using a result on proximity in convex quadratic minimization, we show that this algorithm provides an additive approximation to the optimal objective value of the leader. The additive constant of approximation depends on the flatness constant corresponding to the dimensionality of the follower's decision space and the condition number of the matrix $Q$ defining the quadratic term in the follower's objective function. We show computational evidence indicating the speed advantage as well as that the solution quality guarantee is much better than the worst-case bounds. We extend these results to the case where the follower solves an integer linear program, with an objective perfectly misaligned with that of the leader. Using integer programming proximity, we show that a similar algorithm, used as a heuristic in the literature, provides additive approximation guarantees.

math.OC↗

arXiv2024

Anticipating Oblivious Opponents in Stochastic Games

We present an approach for systematically anticipating the actions and policies employed by \emph{oblivious} environments in concurrent stochastic games, while maximizing a reward function. Our main contribution lies in the synthesis of a finite \emph{information state machine} whose alphabet ranges over the actions of the environment. Each state of the automaton is mapped to a belief state about the policy used by the environment. We introduce a notion of consistency that guarantees that the belief states tracked by our automaton stays within a fixed distance of the precise belief state obtained by knowledge of the full history. We provide methods for checking consistency of an automaton and a synthesis approach which upon successful termination yields such a machine. We show how the information state machine yields an MDP that serves as the starting point for computing optimal policies for maximizing a reward function defined over plays. We present an experimental evaluation over benchmark examples including human activity data for tasks such as cataract surgery and furniture assembly, wherein our approach successfully anticipates the policies and actions of the environment in order to maximize the reward.

cs.AI↗

arXiv2024

Large Language Models Enable Automated Formative Feedback in Human-Robot Interaction Tasks

We claim that LLMs can be paired with formal analysis methods to provide accessible, relevant feedback for HRI tasks. While logic specifications are useful for defining and assessing a task, these representations are not easily interpreted by non-experts. Luckily, LLMs are adept at generating easy-to-understand text that explains difficult concepts. By integrating task assessment outcomes and other contextual information into an LLM prompt, we can effectively synthesize a useful set of recommendations for the learner to improve their performance.

cs.RO↗

arXiv2024

Automated Assessment and Adaptive Multimodal Formative Feedback Improves Psychomotor Skills Training Outcomes in Quadrotor Teleoperation

The workforce will need to continually upskill in order to meet the evolving demands of industry, especially working with robotic and autonomous systems. Current training methods are not scalable and do not adapt to the skills that learners already possess. In this work, we develop a system that automatically assesses learner skill in a quadrotor teleoperation task using temporal logic task specifications. This assessment is used to generate multimodal feedback based on the principles of effective formative feedback. Participants perceived the feedback positively. Those receiving formative feedback viewed the feedback as more actionable compared to receiving summary statistics. Participants in the multimodal feedback condition were more likely to achieve a safe landing and increased their safe landings more over the experiment compared to other feedback conditions. Finally, we identify themes to improve adaptive feedback and discuss and how training for complex psychomotor tasks can be integrated with learning theories.

cs.RO↗

arXiv2024

The Cut-and-Play Algorithm: Computing Nash Equilibria via Outer Approximations

We introduce Cut-and-Play, a practically-efficient algorithm for computing Nash equilibria in simultaneous non-cooperative games where players decide via nonconvex and possibly unbounded optimization problems with separable payoff functions. Our algorithm exploits an intrinsic relationship between the equilibria of the original nonconvex game and the ones of a convexified counterpart. In practice, Cut-and-Play formulates a series of convex approximations of the game and iteratively refines them with cutting planes and branching operations. Our algorithm does not require convexity or continuity of the player's optimization problems and can be integrated with existing optimization software. We test Cut-and-Play on two families of challenging nonconvex games involving discrete decisions and bilevel problems, and we empirically demonstrate that it efficiently computes equilibria while outperforming existing game-specific algorithms.

math.OC↗

arXiv2024

Worst-Case Convergence Time of ML Algorithms via Extreme Value Theory

This paper leverages the statistics of extreme values to predict the worst-case convergence times of machine learning algorithms. Timing is a critical non-functional property of ML systems, and providing the worst-case converge times is essential to guarantee the availability of ML and its services. However, timing properties such as worst-case convergence times (WCCT) are difficult to verify since (1) they are not encoded in the syntax or semantics of underlying programming languages of AI, (2) their evaluations depend on both algorithmic implementations and underlying systems, and (3) their measurements involve uncertainty and noise. Therefore, prevalent formal methods and statistical models fail to provide rich information on the amounts and likelihood of WCCT. Our key observation is that the timing information we seek represents the extreme tail of execution times. Therefore, extreme value theory (EVT), a statistical discipline that focuses on understanding and predicting the distribution of extreme values in the tail of outcomes, provides an ideal framework to model and analyze WCCT in the training and inference phases of ML paradigm. Building upon the mathematical tools from EVT, we propose a practical framework to predict the worst-case timing properties of ML. Over a set of linear ML training algorithms, we show that EVT achieves a better accuracy for predicting WCCTs than relevant statistical methods such as the Bayesian factor. On the set of larger machine learning training algorithms and deep neural network inference, we show the feasibility and usefulness of EVT models to accurately predict WCCTs, their expected return periods, and their likelihood.

cs.SE↗

arXiv2024

Optimal Planning for Timed Partial Order Specifications

This paper addresses the challenge of planning a sequence of tasks to be performed by multiple robots while minimizing the overall completion time subject to timing and precedence constraints. Our approach uses the Timed Partial Orders (TPO) model to specify these constraints. We translate this problem into a Traveling Salesman Problem (TSP) variant with timing and precedent constraints, and we solve it as a Mixed Integer Linear Programming (MILP) problem. Our contributions include a general planning framework for TPO specifications, a MILP formulation accommodating time windows and precedent constraints, its extension to multi-robot scenarios, and a method to quantify plan robustness. We demonstrate our framework on several case studies, including an aircraft turnaround task involving three Jackal robots, highlighting the approach's potential applicability to important real-world problems. Our benchmark results show that our MILP method outperforms state-of-the-art open-source TSP solvers OR-Tools.

cs.RO↗

arXiv2023

An Abstract Model for Branch and Cut

Branch and cut is the dominant paradigm for solving a wide range of mathematical programming problems -- linear or nonlinear -- combining efficient search (via branch and bound) and relaxation-tightening procedures (via cutting planes, or cuts). While there is a wealth of computational experience behind existing cutting strategies, there is simultaneously a relative lack of theoretical explanations for these choices, and for the tradeoffs involved therein. Recent papers have explored abstract models for branching and for comparing cuts with branch and bound. However, to model practice, it is crucial to understand the impact of jointly considering branching and cutting decisions. In this paper, we provide a framework for analyzing how cuts affect the size of branch-and-cut trees, as well as their impact on solution time. Our abstract model captures some of the key characteristics of real-world phenomena in branch-and-cut experiments, regarding whether to generate cuts only at the root or throughout the tree, how many rounds of cuts to add before starting to branch, and why cuts seem to exhibit nonmonotonic effects on the solution process.

math.OC↗

arXiv2023

Integer Programming Games: A Gentle Computational Overview

In this tutorial, we present a computational overview on computing Nash equilibria in Integer Programming Games ($IPG$s), $i.e.$, how to compute solutions for a class of non-cooperative and nonconvex games where each player solves a mixed-integer optimization problem. $IPG$s are a broad class of games extending the modeling power of mixed-integer optimization to multi-agent settings. This class of games includes, for instance, any finite game and any multi-agent extension of traditional combinatorial optimization problems. After providing some background motivation and context of applications, we systematically review and classify the state-of-the-art algorithms to compute Nash equilibria. We propose an essential taxonomy of the algorithmic ingredients needed to compute equilibria, and we describe the theoretical and practical challenges associated with equilibria computation. Finally, we quantitatively and qualitatively compare a sequential Stackelberg game with a simultaneous $IPG$ to highlight the different properties of their solutions.

math.OC↗

arXiv2023

Template-Based Piecewise Affine Regression

We investigate the problem of fitting piecewise affine functions (PWA) to data. Our algorithm divides the input domain into finitely many polyhedral regions whose shapes are specified using a user-defined template such that the data points in each region are fit by an affine function within a desired error bound. We first prove that this problem is NP-hard. Next, we present a top-down algorithm that considers subsets of the overall data set in a systematic manner, trying to fit an affine function for each subset using linear regression. If regression fails on a subset, we extract a minimal set of points that led to a failure in order to split the original index set into smaller subsets. Using a combination of this top-down scheme and a set covering algorithm, we derive an overall approach that is optimal in terms of the number of pieces of the resulting PWA model. We demonstrate our approach on two numerical examples that include PWA approximations of a widely used nonlinear insulin--glucose regulation model and a double inverted pendulum with soft contacts.

eess.SY↗

arXiv2023

Cooperative Security Against Interdependent Risks

Firms in inter-organizational networks such as supply chains or strategic alliances are exposed to interdependent risks. These are risks that are transferable across partner firms. They can be decomposed into intrinsic risks a firm faces from its own operations and extrinsic risks transferred from its partners. Firms broadly have access to two security strategies: either they can independently eliminate both intrinsic and extrinsic risks by securing their links with partners, or alternatively, firms can cooperate with partners to eliminate sources of intrinsic risk in the network. We develop a graph-theoretic model of interdependent security and demonstrate that the network-optimal security strategy can be computed in polynomial time. Then, we use cooperative game-theoretic tools to examine whether and when firms can sustain the network-optimal security strategy via cost-sharing mechanisms that are stable, fair, computable, and implementable via a series of bilateral cost-sharing arrangements. We consider different informational assumptions in the network and show that, when the players know only their own costs, firms have a clear incentive to cooperate globally whereas, in the presence of public information, there may not exist cost-sharing mechanisms that can sustain network-wide cooperation. We then design a novel cost-sharing mechanism: the agreeable allocation, that is easy to compute, bilaterally implementable, ensures stability, and is fair in a well-defined sense. However, the agreeable allocation need not always exist. We then generalize levels of agreeable allocation, with weaker implementability properties but greater existence guarantees.

cs.GT↗