Research map / Bandits and online learning / Contextual bandits and Thompson sampling
Almost Free: Self-concordance in Natural Exponential Families and an Application to Bandits
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Shows that single-parameter natural exponential families with subexponential tails are self-concordant with polynomial-sized parameters, characterizes the self-concordance growth for subgaussian families, and applies this to close gaps for optimistic generalized linear bandit algorithms.
Problem
Whether single-parameter natural exponential families are self-concordant (needed for regret analysis of optimistic GLM bandits), and how the self-concordance parameter grows for such families.
Approach
Proves that single-parameter natural exponential families with subexponential tails are self-concordant with polynomially sized parameters, and gives an exact characterization of the growth rate of the self-concordance parameter for subgaussian families, then applies this to optimistic generalized linear bandits.
Key results
- Single-parameter natural exponential families with subexponential tails are self-concordant with polynomial-sized parameters.
- For subgaussian natural exponential families, an exact characterization of the growth rate of the self-concordance parameter is established.
Experimental setup
Builds on: generalized linear bandits self-concordance analysis of GLMs
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