Computational Lower Bound
The lowest bound on regret achievable under the constraint of polynomial-time algorithms. It is typically higher than the information-theoretic lower bound, and the gap between the two is called the information-computation gap.
Timeline (last 90 days)
Information-theoretic lower bounds characterize the best performance achievable by any algorithm (even exponential-time) without computational resource constraints, corresponding in this problem to Õ(md+k); computational lower bounds, by contrast, assume the algorithm must run in polynomial time, and the resulting bounds are usually larger.
This separation result echoes a series of computational lower bound works in online learning and online convex optimization in recent years, confirming the general phenomenon that "statistical optimality does not necessarily imply computational feasibility."
All Facts (2)
Information-theoretic lower bounds characterize the best performance achievable by any algorithm (even exponential-time) without computational resource constraints, corresponding in this problem to Õ(md+k); computational lower bounds, by contrast, assume the algorithm must run in polynomial time, and the resulting bounds are usually larger.
50%UnverifiedThis separation result echoes a series of computational lower bound works in online learning and online convex optimization in recent years, confirming the general phenomenon that "statistical optimality does not necessarily imply computational feasibility."
50%