7 research outputs found
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
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
A Two-Player Resource-Sharing Game with Asymmetric Information
This paper considers a two-player game where each player chooses a resource
from a finite collection of options. Each resource brings a random reward. Both
players have statistical information regarding the rewards of each resource.
Additionally, there exists an information asymmetry where each player has
knowledge of the reward realizations of different subsets of the resources. If
both players choose the same resource, the reward is divided equally between
them, whereas if they choose different resources, each player gains the full
reward of the resource. We first implement the iterative best response
algorithm to find an -approximate Nash equilibrium for this game.
This method of finding a Nash equilibrium may not be desirable when players do
not trust each other and place no assumptions on the incentives of the
opponent. To handle this case, we solve the problem of maximizing the
worst-case expected utility of the first player. The solution leads to
counter-intuitive insights in certain special cases. To solve the general
version of the problem, we develop an efficient algorithmic solution that
combines online-convex optimization and the drift-plus penalty technique
Online Learning under Budget and ROI Constraints via Weak Adaptivity
We study online learning problems in which a decision maker has to make a
sequence of costly decisions, with the goal of maximizing their expected reward
while adhering to budget and return-on-investment (ROI) constraints. Existing
primal-dual algorithms designed for constrained online learning problems under
adversarial inputs rely on two fundamental assumptions. First, the decision
maker must know beforehand the value of parameters related to the degree of
strict feasibility of the problem (i.e. Slater parameters). Second, a strictly
feasible solution to the offline optimization problem must exist at each round.
Both requirements are unrealistic for practical applications such as bidding in
online ad auctions. In this paper, we show how such assumptions can be
circumvented by endowing standard primal-dual templates with weakly adaptive
regret minimizers. This results in a ``dual-balancing'' framework which ensures
that dual variables stay sufficiently small, even in the absence of knowledge
about Slater's parameter. We prove the first best-of-both-worlds no-regret
guarantees which hold in absence of the two aforementioned assumptions, under
stochastic and adversarial inputs. Finally, we show how to instantiate the
framework to optimally bid in various mechanisms of practical relevance, such
as first- and second-price auctions