119 research outputs found
Distributed Online Optimization with Coupled Inequality Constraints over Unbalanced Directed Networks
This paper studies a distributed online convex optimization problem, where
agents in an unbalanced network cooperatively minimize the sum of their
time-varying local cost functions subject to a coupled inequality constraint.
To solve this problem, we propose a distributed dual subgradient tracking
algorithm, called DUST, which attempts to optimize a dual objective by means of
tracking the primal constraint violations and integrating dual subgradient and
push sum techniques. Different from most existing works, we allow the
underlying network to be unbalanced with a column stochastic mixing matrix. We
show that DUST achieves sublinear dynamic regret and constraint violations,
provided that the accumulated variation of the optimal sequence grows
sublinearly. If the standard Slater's condition is additionally imposed, DUST
acquires a smaller constraint violation bound than the alternative existing
methods applicable to unbalanced networks. Simulations on a plug-in electric
vehicle charging problem demonstrate the superior convergence of DUST
Online Game with Time-Varying Coupled Inequality Constraints
In this paper, online game is studied, where at each time, a group of players
aim at selfishly minimizing their own time-varying cost function simultaneously
subject to time-varying coupled constraints and local feasible set constraints.
Only local cost functions and local constraints are available to individual
players, who can share limited information with their neighbors through a fixed
and connected graph. In addition, players have no prior knowledge of future
cost functions and future local constraint functions. In this setting, a novel
decentralized online learning algorithm is devised based on mirror descent and
a primal-dual strategy. The proposed algorithm can achieve sublinearly bounded
regrets and constraint violation by appropriately choosing decaying stepsizes.
Furthermore, it is shown that the generated sequence of play by the designed
algorithm can converge to the variational GNE of a strongly monotone game, to
which the online game converges. Additionally, a payoff-based case, i.e., in a
bandit feedback setting, is also considered and a new payoff-based learning
policy is devised to generate sublinear regrets and constraint violation.
Finally, the obtained theoretical results are corroborated by numerical
simulations.Comment: arXiv admin note: text overlap with arXiv:2105.0620
Distributed Online Convex Optimization with Time-Varying Coupled Inequality Constraints
This paper considers distributed online optimization with time-varying
coupled inequality constraints. The global objective function is composed of
local convex cost and regularization functions and the coupled constraint
function is the sum of local convex functions. A distributed online primal-dual
dynamic mirror descent algorithm is proposed to solve this problem, where the
local cost, regularization, and constraint functions are held privately and
revealed only after each time slot. Without assuming Slater's condition, we
first derive regret and constraint violation bounds for the algorithm and show
how they depend on the stepsize sequences, the accumulated dynamic variation of
the comparator sequence, the number of agents, and the network connectivity. As
a result, under some natural decreasing stepsize sequences, we prove that the
algorithm achieves sublinear dynamic regret and constraint violation if the
accumulated dynamic variation of the optimal sequence also grows sublinearly.
We also prove that the algorithm achieves sublinear static regret and
constraint violation under mild conditions. Assuming Slater's condition, we
show that the algorithm achieves smaller bounds on the constraint violation. In
addition, smaller bounds on the static regret are achieved when the objective
function is strongly convex. Finally, numerical simulations are provided to
illustrate the effectiveness of the theoretical results
Distributed Online Convex Optimization with an Aggregative Variable
This paper investigates distributed online convex optimization in the
presence of an aggregative variable without any global/central coordinators
over a multi-agent network, where each individual agent is only able to access
partial information of time-varying global loss functions, thus requiring local
information exchanges between neighboring agents. Motivated by many
applications in reality, the considered local loss functions depend not only on
their own decision variables, but also on an aggregative variable, such as the
average of all decision variables. To handle this problem, an Online
Distributed Gradient Tracking algorithm (O-DGT) is proposed with exact gradient
information and it is shown that the dynamic regret is upper bounded by three
terms: a sublinear term, a path variation term, and a gradient variation term.
Meanwhile, the O-DGT algorithm is also analyzed with stochastic/noisy
gradients, showing that the expected dynamic regret has the same upper bound as
the exact gradient case. To our best knowledge, this paper is the first to
study online convex optimization in the presence of an aggregative variable,
which enjoys new characteristics in comparison with the conventional scenario
without the aggregative variable. Finally, a numerical experiment is provided
to corroborate the obtained theoretical results
A Tutorial on Distributed Optimization for Cooperative Robotics: from Setups and Algorithms to Toolboxes and Research Directions
Several interesting problems in multi-robot systems can be cast in the
framework of distributed optimization. Examples include multi-robot task
allocation, vehicle routing, target protection and surveillance. While the
theoretical analysis of distributed optimization algorithms has received
significant attention, its application to cooperative robotics has not been
investigated in detail. In this paper, we show how notable scenarios in
cooperative robotics can be addressed by suitable distributed optimization
setups. Specifically, after a brief introduction on the widely investigated
consensus optimization (most suited for data analytics) and on the
partition-based setup (matching the graph structure in the optimization), we
focus on two distributed settings modeling several scenarios in cooperative
robotics, i.e., the so-called constraint-coupled and aggregative optimization
frameworks. For each one, we consider use-case applications, and we discuss
tailored distributed algorithms with their convergence properties. Then, we
revise state-of-the-art toolboxes allowing for the implementation of
distributed schemes on real networks of robots without central coordinators.
For each use case, we discuss their implementation in these toolboxes and
provide simulations and real experiments on networks of heterogeneous robots
Distributed Online Convex Optimization with Adversarial Constraints: Reduced Cumulative Constraint Violation Bounds under Slater's Condition
This paper considers distributed online convex optimization with adversarial
constraints. In this setting, a network of agents makes decisions at each
round, and then only a portion of the loss function and a coordinate block of
the constraint function are privately revealed to each agent. The loss and
constraint functions are convex and can vary arbitrarily across rounds. The
agents collaborate to minimize network regret and cumulative constraint
violation. A novel distributed online algorithm is proposed and it achieves an
network regret bound and an
network cumulative constraint violation bound, where
is the number of rounds and is a user-defined trade-off
parameter. When Slater's condition holds (i.e, there is a point that strictly
satisfies the inequality constraints), the network cumulative constraint
violation bound is reduced to . Moreover, if the loss
functions are strongly convex, then the network regret bound is reduced to
, and the network cumulative constraint violation bound
is reduced to and without
and with Slater's condition, respectively. To the best of our knowledge, this
paper is the first to achieve reduced (network) cumulative constraint violation
bounds for (distributed) online convex optimization with adversarial
constraints under Slater's condition. Finally, the theoretical results are
verified through numerical simulations
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