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Best Arm Identification in Generalized Linear Bandits via Hybrid Feedback

NeurIPS 2026 · Bandits and online learning › Multi-armed bandits · approach: Best-arm identification in linear bandits · 0 citations (OpenAlex)

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Studies fixed-confidence best arm identification in generalized linear bandits with hybrid reward and dueling feedback, combining a likelihood-ratio confidence ellipsoid with a Track-and-Stop allocation (HyTS-GLB) and a cost-aware variant.

Problem

Fixed-confidence best arm identification when the learner can query either absolute reward feedback from single arms or relative dueling feedback from arm pairs, both modeled as GLMs sharing one latent parameter.

Approach

Builds a single ellipsoidal confidence set from a likelihood-ratio confidence sequence by aggregating reward and dueling curvature into one information matrix under self-concordance, then runs Track-and-Stop over the joint space of arms and arm pairs, with a cost-normalized variant for heterogeneous query costs.

Key results

• HyTS-GLB achieves the smallest mean stopping time for d=4,6,10 and outperforms RageGLM and ReTS-GLB across all dimensions, while DuelTS-GLB is slightly better at d=2,8.
• Cost-aware HyTS-GLB uniformly reduces total acquisition cost relative to standard HyTS-GLB by shifting samples toward the cheaper modality (K=3, d=2).
• Stopping-time bound of order T*(theta)(log(1/delta)+d log T* + d loglog(e/delta)) with high probability.

Surprising findings

• GLGapE did not terminate within the simulation budget in the experiments.

Limitations

• Stopping-time guarantees carry conservative constants and logarithmic factors; the design matrix is a conservative approximation of the Fisher information.
• The information-theoretic lower bound is only a local comparison, not full instance optimality for hybrid GLMs.
• Experiments are limited to synthetic instances under a logistic model with 10 runs.

Experimental setup

Datasets: synthetic bandit instances (logistic observation model)

Benchmarks: synthetic hybrid GLB instances with d in {2,4,6,8,10}

Metrics: stopping time total acquisition cost

Baselines: RageGLM ReTS-GLB DuelTS-GLB random hybrid baseline GLGapE

Builds on: Track-and-Stop likelihood-ratio confidence sequences for self-concordant GLMs RageGLM

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