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Robust Neural Contextual Bandit against Adversarial Corruptions
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Proposes R-NeuralUCB, a neural contextual bandit that uses arm-specific, uncertainty-weighted gradient descent to resist adversarial reward corruptions, with regret bounds that drop the arm-separateness assumption.
Problem
Neural contextual bandits are vulnerable to adversarial corruptions of observed arm rewards, and existing neural bandit theory relies on arm-separateness assumptions that fail when adversaries choose duplicate arms.
Approach
Trains arm-specific neural networks with per-sample weights derived from NTK/gradient uncertainty (downweighting high-uncertainty samples and regularizing toward initialization for uncertain arms), combined with a UCB exploration rule; the regret analysis uses NTK Gram matrices over unique arms so no arm-separateness assumption is needed.
Key results
- R-NeuralUCB achieves a regret bound of O~(ed sqrt(T) + C beta^-1 ed), removing the known-corruption-level assumption and the arm-separateness assumption.
- On MNIST with C=2000, R-NeuralUCB reaches about 1989 cumulative regret versus about 2103 for NeuralUCB-WGD in the parameter study (lambda=0.001 setting).
- Across MovieLens, Amazon and MNIST experiments, R-NeuralUCB outperforms NeuralUCB-WGD and conventional neural baselines (Neural-UCB, Neural-TS) and linear baselines under 20% and 50% corruption settings.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| set λ from 0.01 to 0.001 (ablation) | R-NeuralUCB · MNIST (C=2000) | cumulative regret: 2501 ±93 -> 1989 ±67 | Helped |
| set λ from 0.001 to 0.0001 (ablation) | R-NeuralUCB · MNIST (C=2000) | cumulative regret: 1989 ±67 -> 2127 ±92 | Hurt |
| set ν from 0.5 to 0.1 (ablation) | R-NeuralUCB · MNIST (C=2000) | cumulative regret: 2163 ±88 -> 1989 ±67 | Helped |
| set ν from 0.1 to 0.05 (ablation) | R-NeuralUCB · MNIST (C=2000) | cumulative regret: 1989 ±67 -> 2197 ±65 | Hurt |
Surprising findings
- On the Amazon dataset the performance gap among algorithms narrows under 50% corruption, which the authors attribute to the task becoming much harder (regret up to about 8000).
Limitations
- No theoretical lower bound for neural bandits with corruptions is provided.
- Regret bound's corruption term depends on beta^-1, the minimum fraction term, which can be large.
- Experiments use a two-layer network and simulated corruptions only.
Experimental setup
Datasets: MovieLens 20M Amazon Recommendation (McAuley 2014) MNIST
Benchmarks: MovieLens Amazon MNIST
Metrics: cumulative regret
Baselines: Lin-UCB CW-OFUL Neural-UCB Neural-TS NeuralUCB-WGD
Builds on: NeuralUCB CW-OFUL NTK regression Neural-TS
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