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Lower Bounds on Cross-Entropy Loss in the Presence of Test-time Adversaries
Arjun Nitin Bhagoji · Daniel Cullina · Vikash Sehwag · Prateek Mittal

Thu Jul 22 07:25 AM -- 07:30 AM (PDT) @
in Adversarial Learning 2 »

Understanding the fundamental limits of robust supervised learning has emerged as a problem of immense interest, from both practical and theoretical standpoints. In particular, it is critical to determine classifier-agnostic bounds on the training loss to establish when learning is possible. In this paper, we determine optimal lower bounds on the cross-entropy loss in the presence of test-time adversaries, along with the corresponding optimal classification outputs. Our formulation of the bound as a solution to an optimization problem is general enough to encompass any loss function depending on soft classifier outputs. We also propose and provide a proof of correctness for a bespoke algorithm to compute this lower bound efficiently, allowing us to determine lower bounds for multiple practical datasets of interest. We use our lower bounds as a diagnostic tool to determine the effectiveness of current robust training methods and find a gap from optimality at larger budgets. Finally, we investigate the possibility of using of optimal classification outputs as soft labels to empirically improve robust training.

Keywords: Adversarial Examples · Algorithms

Author Information

Arjun Nitin Bhagoji (University of Chicago)
Daniel Cullina (Penn State University)
Vikash Sehwag (Princeton University)
Prateek Mittal (Princeton University)

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