202 research outputs found
Asymmetric Feedback Learning in Online Convex Games
This paper considers online convex games involving multiple agents that aim
to minimize their own cost functions using locally available feedback. A common
assumption in the study of such games is that the agents are symmetric, meaning
that they have access to the same type of information or feedback. Here we lift
this assumption, which is often violated in practice, and instead consider
asymmetric agents; specifically, we assume some agents have access to
first-order gradient feedback and others have access to the zeroth-order
oracles (cost function evaluations). We propose an asymmetric feedback learning
algorithm that combines the agent feedback mechanisms. We analyze the regret
and Nash equilibrium convergence of this algorithm for convex games and
strongly monotone games, respectively. Specifically, we show that our algorithm
always performs between pure first-order and zeroth-order methods, and can
match the performance of these two extremes by adjusting the number of agents
with access to zeroth-order oracles. Therefore, our algorithm incorporates the
pure first-order and zeroth-order methods as special cases. We provide
numerical experiments on an online market problem for both deterministic and
risk-averse games to demonstrate the performance of the proposed algorithm.Comment: 16page
Small Errors in Random Zeroth Order Optimization are Imaginary
The vast majority of zeroth order optimization methods try to imitate first
order methods via some smooth approximation of the gradient. Here, the smaller
the smoothing parameter, the smaller the gradient approximation error. We show
that for the majority of zeroth order methods this smoothing parameter can
however not be chosen arbitrarily small as numerical cancellation errors will
dominate. As such, theoretical and numerical performance could differ
significantly. Using classical tools from numerical differentiation we will
propose a new smoothed approximation of the gradient that can be integrated
into general zeroth order algorithmic frameworks. Since the proposed smoothed
approximation does not suffer from cancellation errors, the smoothing parameter
(and hence the approximation error) can be made arbitrarily small. Sublinear
convergence rates for algorithms based on our smoothed approximation are
proved. Numerical experiments are also presented to demonstrate the superiority
of algorithms based on the proposed approximation.Comment: New: Figure 3.
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