Binary Worst-Case Theorem for the Jensen–Shannon Chain-Rule Ratio
Binary Worst-Case Theorem for the Jensen–Shannon Chain-Rule Ratio
A complete proof that the worst-case Jensen–Shannon chain-rule ratio over binary triples is a universal constant, obtained via martingale decomposition, Dinkelbach linearization, and concave-envelope support reduction to two-by-two-by-two distributions. The sharp constant is computed to high precision through a KKT system with hidden quadratic structure.
support reduction, fractional programming, chain-rule inequality, Jensen–Shannon divergence, martingale optimization, sharp constant, Jensen-Shannon divergence, martingale decomposition, Dinkelbach linearization, information ratio, rare-event asymptotics, f-divergence, concave envelope, chain rule, binary alphabet
support reduction, fractional programming, chain-rule inequality, Jensen–Shannon divergence, martingale optimization, sharp constant, Jensen-Shannon divergence, martingale decomposition, Dinkelbach linearization, information ratio, rare-event asymptotics, f-divergence, concave envelope, chain rule, binary alphabet
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