26 research outputs found
A Geometric Proof of Calibration
We provide yet another proof of the existence of calibrated forecasters; it
has two merits. First, it is valid for an arbitrary finite number of outcomes.
Second, it is short and simple and it follows from a direct application of
Blackwell's approachability theorem to carefully chosen vector-valued payoff
function and convex target set. Our proof captures the essence of existing
proofs based on approachability (e.g., the proof by Foster, 1999 in case of
binary outcomes) and highlights the intrinsic connection between
approachability and calibration
Approachability in unknown games: Online learning meets multi-objective optimization
In the standard setting of approachability there are two players and a target
set. The players play repeatedly a known vector-valued game where the first
player wants to have the average vector-valued payoff converge to the target
set which the other player tries to exclude it from this set. We revisit this
setting in the spirit of online learning and do not assume that the first
player knows the game structure: she receives an arbitrary vector-valued reward
vector at every round. She wishes to approach the smallest ("best") possible
set given the observed average payoffs in hindsight. This extension of the
standard setting has implications even when the original target set is not
approachable and when it is not obvious which expansion of it should be
approached instead. We show that it is impossible, in general, to approach the
best target set in hindsight and propose achievable though ambitious
alternative goals. We further propose a concrete strategy to approach these
goals. Our method does not require projection onto a target set and amounts to
switching between scalar regret minimization algorithms that are performed in
episodes. Applications to global cost minimization and to approachability under
sample path constraints are considered
Learning Aided Optimization for Energy Harvesting Devices with Outdated State Information
This paper considers utility optimal power control for energy harvesting
wireless devices with a finite capacity battery. The distribution information
of the underlying wireless environment and harvestable energy is unknown and
only outdated system state information is known at the device controller. This
scenario shares similarity with Lyapunov opportunistic optimization and online
learning but is different from both. By a novel combination of Zinkevich's
online gradient learning technique and the drift-plus-penalty technique from
Lyapunov opportunistic optimization, this paper proposes a learning-aided
algorithm that achieves utility within of the optimal, for any
desired , by using a battery with an capacity. The
proposed algorithm has low complexity and makes power investment decisions
based on system history, without requiring knowledge of the system state or its
probability distribution.Comment: This version extends v1 (our INFOCOM 2018 paper): (1) add a new
section (Section V) to study the case where utility functions are non-i.i.d.
arbitrarily varying (2) add more simulation experiments. The current version
is published in IEEE/ACM Transactions on Networkin