Unverified50% confidenceFactExact time
In a continuous convex action space, discretizing the action space and applying the discrete algorithm can yield Õ(md+k) regret, but the number of grid points required grows exponentially with the dimension d, making the algorithm infeasible in polynomial time.
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10/15/2026
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UnverifiedNaively approximating the infinite-dimensional functional gradient causes the algorithm to converge to the wrong location, introducing systematic bias.79% similarUnverifiedWhen the parameter space is generalized from finite dimensions to an infinite-dimensional function space, the inner optimization problem of maximizing the acquisition function becomes neither exhaustively searchable nor readily amenable to direct gradient descent.77% similarUnverifiedInformation-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.77% similarUnverifiedFor practical algorithm design, when the dimension d is large and the number of switches k is non-negligible, accepting Õ(dk)-level regret or seeking additional structural assumptions may be a more pragmatic direction than relying on discretization or exact optimization.74% similarUnverifiedThere is an essential separation between the information-theoretically optimal regret Õ(md+k) and the regret achievable in polynomial time; this gap is inherent to computational complexity rather than a shortcoming of algorithm design.74% similar
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