南京大学：《高级优化 Advanced Optimization》课程教学资源（讲稿）Lecture 12 Stochastic Bandits - MAB, UCB, linear bandits, self-normalized concentration, generalized linear bandits

Upper Confidence Bound ·UCB With high probability u(a)<UCB:(a)=p(a)+B(a) UCB:(1)? UCB:(2) UCB:(3)￥3(3 3,(1) u(2)●3，(2 : (1)● (2)· u(1)● Optimism in Face of Uncertainty:at =arg maxaEIK]UCB(a) Advanced Optimization(Fall 2023) Lecture 12.Stochastic Bandits 16

Advanced Optimization (Fall 2023) Lecture 12. Stochastic Bandits 16 Upper Confidence Bound • UCB

Upper Confidence Bound ·UCB With high probability u(a)<UCB:(a)=(a)+B(a) UCB:(1) UCB:(2) UCB(3)界3③) 3,(10 4(2)·3,(2) : t(1)● (2)● (1)● Optimism in Face of Uncertainty:at=arg maxaEIK]UCB(a) Advanced Optimization(Fall 2023) Lecture 12.Stochastic Bandits 17

Advanced Optimization (Fall 2023) Lecture 12. Stochastic Bandits 17 Upper Confidence Bound • UCB