3 research outputs found
Maximal-Capacity Discrete Memoryless Channel Identification
The problem of identifying the channel with the highest capacity among
several discrete memoryless channels (DMCs) is considered. The problem is cast
as a pure-exploration multi-armed bandit problem, which follows the practical
use of training sequences to sense the communication channel statistics. A
capacity estimator is proposed and tight confidence bounds on the estimator
error are derived. Based on this capacity estimator, a gap-elimination
algorithm termed BestChanID is proposed, which is oblivious to the
capacity-achieving input distribution and is guaranteed to output the DMC with
the largest capacity, with a desired confidence. Furthermore, two additional
algorithms NaiveChanSel and MedianChanEl, that output with certain confidence a
DMC with capacity close to the maximal, are introduced. Each of those
algorithms is beneficial in a different regime and can be used as a subroutine
in BestChanID. The sample complexity of all algorithms is analyzed as a
function of the desired confidence parameter, the number of channels, and the
channels' input and output alphabet sizes. The cost of best channel
identification is shown to scale quadratically with the alphabet size, and a
fundamental lower bound for the required number of channel senses to identify
the best channel with a certain confidence is derived
The (Surprising) Sample Optimality of Greedy Procedures for Large-Scale Ranking and Selection
Ranking and selection (R&S), which aims to select the best alternative with
the largest mean performance from a finite set of alternatives, is a classic
research topic in simulation optimization. Recently, considerable attention has
turned towards the large-scale variant of the R&S problem which involves a
large number of alternatives. Ideal large-scale R&S procedures should be sample
optimal, i.e., the total sample size required to deliver an asymptotically
non-zero probability of correct selection (PCS) grows at the minimal order
(linear order) in the number of alternatives, but not many procedures in the
literature are sample optimal. Surprisingly, we discover that the na\"ive
greedy procedure, which keeps sampling the alternative with the largest running
average, performs strikingly well and appears sample optimal. To understand
this discovery, we develop a new boundary-crossing perspective and prove that
the greedy procedure is indeed sample optimal. We further show that the derived
PCS lower bound is asymptotically tight for the slippage configuration of means
with a common variance. Moreover, we propose the explore-first greedy (EFG)
procedure and its enhanced version (EFG procedure) by adding an exploration
phase to the na\"ive greedy procedure. Both procedures are proven to be sample
optimal and consistent. Last, we conduct extensive numerical experiments to
empirically understand the performance of our greedy procedures in solving
large-scale R&S problems