MaxHedge: Maximising a Maximum Online
This work addresses online combinatorial optimization problems for scenarios with dynamic environments and resource constraints, though it appears incremental as it builds upon existing online learning frameworks.
The authors tackled the problem of online subset selection under energy constraints, where rewards and costs change over time, by proposing MaxHedge, an efficient algorithm that maximizes cumulative profit by balancing maximum reward and cost minimization.
We introduce a new online learning framework where, at each trial, the learner is required to select a subset of actions from a given known action set. Each action is associated with an energy value, a reward and a cost. The sum of the energies of the actions selected cannot exceed a given energy budget. The goal is to maximise the cumulative profit, where the profit obtained on a single trial is defined as the difference between the maximum reward among the selected actions and the sum of their costs. Action energy values and the budget are known and fixed. All rewards and costs associated with each action change over time and are revealed at each trial only after the learner's selection of actions. Our framework encompasses several online learning problems where the environment changes over time; and the solution trades-off between minimising the costs and maximising the maximum reward of the selected subset of actions, while being constrained to an action energy budget. The algorithm that we propose is efficient and general in that it may be specialised to multiple natural online combinatorial problems.