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Found 21 papers, 1 papers with code
Dissipative Gradient Descent Ascent Method: A Control Theory Inspired Algorithm for Min-max Optimization
Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e. g., in bilinear settings.
Learning safety critics via a non-contractive binary bellman operator
To that end, we study the properties of the binary safety critic associated with a deterministic dynamical system that seeks to avoid reaching an unsafe region.
Recurrence of Nonlinear Control Systems: Entropy and Bit Rates
In this paper, we introduce the notion of recurrence entropy in the context of nonlinear control systems.
Closed-Loop Motion Planning for Differentially Flat Systems: A Time-Varying Optimization Framework
The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to follow, and an online/closed-loop stage, tracking, that corrects for unmodeled dynamics and disturbances.
Early Neuron Alignment in Two-layer ReLU Networks with Small Initialization
Our analysis shows that, during the early phase of training, neurons in the first layer try to align with either the positive data or the negative data, depending on its corresponding weight on the second layer.
Necessary and Sufficient Conditions for Simultaneous State and Input Recovery of Linear Systems with Sparse Inputs by $\ell_1$-Minimization
In this work, we provide (1) the first characterization of necessary and sufficient conditions for the existence and uniqueness of sparse inputs to an LDS, (2) the first necessary and sufficient conditions for a linear program to recover both an unknown initial state and a sparse input, and (3) simple, interpretable recovery conditions in terms of the LDS parameters.
A Frequency Domain Analysis of Slow Coherency in Networked Systems
Network coherence generally refers to the emergence of simple aggregated dynamical behaviours, despite heterogeneity in the dynamics of the subsystems that constitute the network.
Constrained Reinforcement Learning via Dissipative Saddle Flow Dynamics
In constrained reinforcement learning (C-RL), an agent seeks to learn from the environment a policy that maximizes the expected cumulative reward while satisfying minimum requirements in secondary cumulative reward constraints.
Learning Coherent Clusters in Weakly-Connected Network Systems
We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components.
Spectral clustering and model reduction for weakly-connected coherent network systems
We propose a novel model-reduction methodology for large-scale dynamic networks with tightly-connected components.
Model-free Learning of Regions of Attraction via Recurrent Sets
We define a set to be $\tau$-recurrent (resp.
Closed-Form Minkowski Sum Approximations for Efficient Optimization-Based Collision Avoidance
Motion planning methods for autonomous systems based on nonlinear programming offer great flexibility in incorporating various dynamics, objectives, and constraints.
Reinforcement Learning with Almost Sure Constraints
We argue that stationary policies are not sufficient for solving this problem, and that a rich class of policies can be found by endowing the controller with a scalar quantity, so called budget, that tracks how close the agent is to violating the constraint.
Learning to Act Safely with Limited Exposure and Almost Sure Certainty
Our analysis further highlights a trade-off between the time lag for the underlying MDP necessary to detect unsafe actions, and the level of exposure to unsafe events.
Convergence and Implicit Bias of Gradient Flow on Overparametrized Linear Networks
Firstly, we show that the squared loss converges exponentially to its optimum at a rate that depends on the level of imbalance and the margin of the initialization.
Voltage Collapse Stabilization in Star DC Networks
Voltage collapse is a type of blackout-inducing dynamic instability that occurs when power demand exceeds the maximum power that can be transferred through a network.
Coherence and Concentration in Tightly-Connected Networks
More precisely, for a networked system with linear dynamics and coupling, we show that, as the network connectivity grows, the system transfer matrix converges to a rank-one transfer matrix representing the coherent behavior.
On the Explicit Role of Initialization on the Convergence and Generalization Properties of Overparametrized Linear Networks
In this paper, we present a novel analysis of overparametrized single-hidden layer linear networks, which formally connects initialization, optimization, and overparametrization with generalization performance.
Assured RL: Reinforcement Learning with Almost Sure Constraints
We consider the problem of finding optimal policies for a Markov Decision Process with almost sure constraints on state transitions and action triplets.
Learning to be safe, in finite time
More precisely, by defining a handicap metric that counts the number of unsafe actions, we provide an algorithm for discarding unsafe machines (or actions), with probability one, that achieves constant handicap.
What is the Largest Sparsity Pattern that Can Be Recovered by 1-Norm Minimization?
In the case of the partial discrete Fourier transform, our characterization of the largest sparsity pattern that can be recovered requires the unknown signal to be real and its dimension to be a prime number.
