Queuing network control determines the allocation of scarce resources to manage congestion, a fundamental problem in manufacturing, communications, and healthcare.

Deterministic We shows Lemma Given >0, ther I and PoF (G,I,0) 1 .

Figure 2: RN "100) when structure (see(A)stationary (B)altered T{3and2T{3as

Lemma 2.Suppose Assumptions 1 and 2 hold.

Foreacharma, letr(a) and cj(a) be, resp., the meanrewardandmeanresource-j consumption,i.e.,(r(a);c1(a),..., cd(a)):=Eo Da[o].We sometimeswriter =( r(a): a 2 [K])andcj =( cj(a): a 2 [K])asvectorsoverarms. Second, weuseatighterversionof Eq. (3.6) (see AppendixD.3):

Figure 2 shows SLSQPand COBYLArunningontheexamplefrom Figure 1.

We develop a class of informationtheoretic Bayesian regret bounds that nearly match existing lower bounds on a variety ofproblem instances, demonstrating theadaptivity ofIDS. Toefficiently implement sparse IDS, we propose an empirical Bayesian approach for sparse posterior sampling using a spike-and-slab Gaussian-Laplace prior. Numerical results demonstrate significant regretreductions bysparseIDSrelativetoseveral baselines.