23 research outputs found
An efficient approach for nonconvex semidefinite optimization via customized alternating direction method of multipliers
We investigate a class of general combinatorial graph problems, including
MAX-CUT and community detection, reformulated as quadratic objectives over
nonconvex constraints and solved via the alternating direction method of
multipliers (ADMM).
We propose two reformulations: one using vector variables and a binary
constraint, and the other further reformulating the Burer-Monteiro form for
simpler subproblems.
Despite the nonconvex constraint, we prove the ADMM iterates converge to a
stationary point in both formulations, under mild assumptions.
Additionally, recent work suggests that in this latter form, when the matrix
factors are wide enough, local optimum with high probability is also the global
optimum.
To demonstrate the scalability of our algorithm, we include results for
MAX-CUT, community detection, and image segmentation benchmark and simulated
examples.Comment: arXiv admin note: text overlap with arXiv:1805.1067
Wasserstein Distributionally Robust Control Barrier Function using Conditional Value-at-Risk with Differentiable Convex Programming
Control Barrier functions (CBFs) have attracted extensive attention for
designing safe controllers for their deployment in real-world safety-critical
systems. However, the perception of the surrounding environment is often
subject to stochasticity and further distributional shift from the nominal one.
In this paper, we present distributional robust CBF (DR-CBF) to achieve
resilience under distributional shift while keeping the advantages of CBF, such
as computational efficacy and forward invariance.
To achieve this goal, we first propose a single-level convex reformulation to
estimate the conditional value at risk (CVaR) of the safety constraints under
distributional shift measured by a Wasserstein metric, which is by nature
tri-level programming. Moreover, to construct a control barrier condition to
enforce the forward invariance of the CVaR, the technique of differentiable
convex programming is applied to enable differentiation through the
optimization layer of CVaR estimation. We also provide an approximate variant
of DR-CBF for higher-order systems. Simulation results are presented to
validate the chance-constrained safety guarantee under the distributional shift
in both first and second-order systems
Scaling Up Multiagent Reinforcement Learning for Robotic Systems: Learn an Adaptive Sparse Communication Graph
The complexity of multiagent reinforcement learning (MARL) in multiagent
systems increases exponentially with respect to the agent number. This
scalability issue prevents MARL from being applied in large-scale multiagent
systems. However, one critical feature in MARL that is often neglected is that
the interactions between agents are quite sparse. Without exploiting this
sparsity structure, existing works aggregate information from all of the agents
and thus have a high sample complexity. To address this issue, we propose an
adaptive sparse attention mechanism by generalizing a sparsity-inducing
activation function. Then a sparse communication graph in MARL is learned by
graph neural networks based on this new attention mechanism. Through this
sparsity structure, the agents can communicate in an effective as well as
efficient way via only selectively attending to agents that matter the most and
thus the scale of the MARL problem is reduced with little optimality
compromised. Comparative results show that our algorithm can learn an
interpretable sparse structure and outperforms previous works by a significant
margin on applications involving a large-scale multiagent system
Joint Estimation of OD Demands and Cost Functions in Transportation Networks from Data
Existing work has tackled the problem of estimating Origin-Destination (OD)
demands and recovering travel latency functions in transportation networks
under the Wardropian assumption. The ultimate objective is to derive an
accurate predictive model of the network to enable optimization and control.
However, these two problems are typically treated separately and estimation is
based on parametric models. In this paper, we propose a method to jointly
recover nonparametric travel latency cost functions and estimate OD demands
using traffic flow data. We formulate the problem as a bilevel optimization
problem and develop an iterative first-order optimization algorithm to solve
it. A numerical example using the Braess Network is presented to demonstrate
the effectiveness of our method.Comment: To appear at the Proceedings of the 58th IEEE Conference on Decision
and Contro
Optimal composition of heterogeneous multi-agent teams for coverage problems with performance bound guarantees
First author draf