Bandits

We study a bandit version of phase retrieval where the learner chooses actions (At)nt=1 in the d-dimensional unit ball and the expected reward is hAt,?i2 with? 2 Rd an unknown parameter vector. We prove an upper bound on the minimax cumulative regret in this problem of (d p n), which matches known lower bounds up to logarithmic factors and improves on the best known upper bound by a factor of p d. We also show that the minimax simple regret is (d/ p n) and that this is only achievable by an adaptive algorithm. Our analysis shows that an apparently convincing heuristic for guessing lower bounds can be misleading and that uniform bounds on the information ratio for information-directed sampling [Russo and Van Roy, 2014] are not sufficient for optimal regret.

We introduce point affiliation into feature upsampling, a notion that describes the affiliation of each upsampled point to a semantic cluster formed by local decoder feature points with semantic similarity. By rethinking point affiliation, we present a generic formulation for generating upsampling kernels. The kernels encourage not only semantic smoothness but also boundary sharpness in the upsampled feature maps. Such properties are particularly useful for some dense prediction tasks such as semantic segmentation. The key idea of our formulation is to generate similarity-aware kernels by comparing the similarity between each encoder feature point and the spatially associated local region of decoder features. In this way, the encoder feature point can function as a cue to inform the semantic cluster of upsampled feature points. To embody the formulation, we further instantiate a lightweight upsampling operator, termed Similarity-Aware Point Affiliation (SAPA), and investigate its variants. SAPA invites consistent performance improvements on a number of dense prediction tasks, including semantic segmentation, object detection, depth estimation, and image matting. Code is available at: https://github.com/poppinace/sapa

Previous language model pre-training methods have uniformly applied a next-token prediction loss to all training tokens.

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