Online Stochastic Bin Packing
Varun Gupta, Ana Radovanovic

TL;DR
This paper introduces the first distribution-oblivious algorithms for online stochastic bin packing that achieve sublinear additive regret for all distributions, including non-i.i.d. sequences, improving over previous heuristics.
Contribution
It presents a novel family of algorithms inspired by convex optimization that are distribution-oblivious and achieve $ ext{O}( oot{T} ext{)}$ regret for all item size distributions, including non-i.i.d. sequences.
Findings
Achieves $ ext{O}( oot{T} ext{)}$ additive regret for all distributions.
Extends regret bounds to continuous distributions with bounded density.
Provides the first regret bounds for non-i.i.d. input sequences.
Abstract
Bin packing is an algorithmic problem that arises in diverse applications such as remnant inventory systems, shipping logistics, and appointment scheduling. In its simplest variant, a sequence of items (e.g., orders for raw material, packages for delivery) is revealed one at a time, and each item must be packed on arrival in an available bin (e.g., remnant pieces of raw material in inventory, shipping containers). The sizes of items are i.i.d. samples from an unknown distribution, but the sizes are known when the items arrive. The goal is to minimize the number of non-empty bins (equivalently waste, defined to be the total unused space in non-empty bins). This problem has been extensively studied in the Operations Research and Theoretical Computer Science communities, yet all existing heuristics either rely on learning the distribution or exhibit additive suboptimality…
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Taxonomy
TopicsOptimization and Search Problems · Optimization and Packing Problems · Complexity and Algorithms in Graphs
