New 'identity-truthful' algorithm beats 0.5 benchmark in online decision-making

Researchers Tomer Ezra and Adar Kantor have published a paper on arXiv (2607.19964) tackling a fundamental problem in online decision-making: Bayesian online selection. In this setting, a decision-maker observes a sequence of stochastic rewards and must immediately accept or reject each one. Traditionally, algorithms know both the reward value and the distribution it came from (its identity). The new twist? The decision-maker sees the value but learns the identity only after deciding—a constraint they call identity-truthfulness. This models real-world scenarios like auction bidders or job applicants where you see an offer but not who made it until you decide.

The authors define the identity-truthfulness gap as the best possible worst-case approximation an identity-truthful algorithm can achieve compared to the optimal online algorithm that knows the order of arrivals. They prove this gap is strictly greater than 0.5, outperforming the identity-blindness gap (exactly 0.5) from prior work. An upper bound of 0.81 is also established, below the 0.829 bound on the order-competitive ratio. Importantly, they show that identity-truthfulness breaks the usual connection between online algorithms and pricing mechanisms: for some instances, no pricing mechanism can implement the optimal identity-truthful algorithm. This has implications for prophet inequality problems and posted-price designs.