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QK k=1[ρk,) is sufficient for ensuring V1:T,k ρk whenever possible, thanks to theminu U operator in (1). Altogether,gMO with suitably chosenρ,U captures Pareto-optimality.15 We start by addressing (5.2). In addition, the solutionx, defined asx (s1,rl) = x (s2,ll) = 1/2 and x (s,a) = 0 for all20 other s,a, is optimal to(PM). WechoseQ = L/ K to optimize the dependence on L,K in the regret order bound in Theorem39 3.1.