Browsing by Subject "Lexicographic optimality"

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Open Access
The biobjective multiarmed bandit: learning approximate lexicographic optimal allocations
(TÜBİTAK, 2019) Tekin, Cem
We consider a biobjective sequential decision-making problem where an allocation (arm) is called ϵ lexicographic optimal if its expected reward in the first objective is at most ϵ smaller than the highest expected reward, and its expected reward in the second objective is at least the expected reward of a lexicographic optimal arm. The goal of the learner is to select arms that are ϵ lexicographic optimal as much as possible without knowing the arm reward distributions beforehand. For this problem, we first show that the learner’s goal is equivalent to minimizing the ϵ lexicographic regret, and then, propose a learning algorithm whose ϵ lexicographic gap-dependent regret is bounded and gap-independent regret is sublinear in the number of rounds with high probability. Then, we apply the proposed model and algorithm for dynamic rate and channel selection in a cognitive radio network with imperfect channel sensing. Our results show that the proposed algorithm is able to learn the approximate lexicographic optimal rate–channel pair that simultaneously minimizes the primary user interference and maximizes the secondary user throughput.
Open Access
Multi-objective multi-armed bandit with lexicographically ordered and satisficing objectives
(Springer, 2021-06) Hüyük, A.; Tekin, Cem
We consider multi-objective multi-armed bandit with (i) lexicographically ordered and (ii) satisficing objectives. In the first problem, the goal is to select arms that are lexicographic optimal as much as possible without knowing the arm reward distributions beforehand. We capture this goal by defining a multi-dimensional form of regret that measures the loss due to not selecting lexicographic optimal arms, and then, propose an algorithm that achieves O~(T2/3) gap-free regret and prove a regret lower bound of Ω(T2/3). We also consider two additional settings where the learner has prior information on the expected arm rewards. In the first setting, the learner only knows for each objective the lexicographic optimal expected reward. In the second setting, it only knows for each objective a near-lexicographic optimal expected reward. For both settings, we prove that the learner achieves expected regret uniformly bounded in time. Then, we show that the algorithm we propose for the second setting of lexicographically ordered objectives with prior information also attains bounded regret for satisficing objectives. Finally, we experimentally evaluate the proposed algorithms in a variety of multi-objective learning problems.