# Contextual Bilateral Trade

With only one-bit feedback, contextual search and contextual bilateral trade had left a visible gap between their upper bounds and the known lower bounds. A single trace-square-root potential now handles both problems, giving worst-case regret within a constant factor of the existing lower bounds, plus Bayesian bounds that depend only on prior covariance matrices and hold at every horizon.

With only one-bit feedback, contextual search and contextual bilateral trade had left a visible gap between their upper bounds and the known lower bounds. A single trace-square-root potential now handles both problems, giving worst-case regret within a constant factor of the existing lower bounds, plus Bayesian bounds that depend only on prior covariance matrices and hold at every horizon.