Vector quantization (VQ) techniques are widely used in similarity search for
data compression, fast metric computation and etc. Originally designed for
Euclidean distance, existing VQ techniques (e.g., PQ, AQ) explicitly or
implicitly minimize the quantization error. In this paper, we present a new
angle to analyze the quantization error, which decomposes the quantization
error into norm error and direction error. We show that quantization errors in
norm have much higher influence on inner products than quantization errors in
direction, and small quantization error does not necessarily lead to good
performance in maximum inner product search (MIPS). Based on this observation,
we propose norm-explicit quantization (NEQ) --- a general paradigm that
improves existing VQ techniques for MIPS. NEQ quantizes the norms of items in a
dataset explicitly to reduce errors in norm, which is crucial for MIPS. For the
direction vectors, NEQ can simply reuse an existing VQ technique to quantize
them without modification. We conducted extensive experiments on a variety of
datasets and parameter configurations. The experimental results show that NEQ
improves the performance of various VQ techniques for MIPS, including PQ, OPQ,
RQ and AQ.

本文提出了一种基于范数误差和方向误差的定量化误差的新方法，指出在最大内积搜索（MIPS）中量化误差在范数方面的影响大于在方向上的影响，因此提出了内部明确的基于规范的矢量量化（NEQ）用于 MIPS。该方法可以明显减小需要搜索的大型数据集，同时提高 PQ，OPQ，RQ 和 AQ 等 VQ 技术的性能。

范数显式量化：改进向量量化获得更佳内积搜索

Norm-Explicit Quantization: Improving Vector Quantization for Maximum  Inner Product Search

Generalized Linear Bandits (GLBs), a natural extension of the stochastic
linear bandits, has been popular and successful in recent years. However,
existing GLBs scale poorly with the number of rounds and the number of arms,
limiting their utility in practice. This paper proposes new, scalable solutions
to the GLB problem in two respects. First, unlike existing GLBs, whose
per-time-step space and time complexity grow at least linearly with time $t$,
we propose a new algorithm that performs online computations to enjoy a
constant space and time complexity. At its heart is a novel Generalized Linear
extension of the Online-to-confidence-set Conversion (GLOC method) that takes
\emph{any} online learning algorithm and turns it into a GLB algorithm. As a
special case, we apply GLOC to the online Newton step algorithm, which results
in a low-regret GLB algorithm with much lower time and memory complexity than
prior work. Second, for the case where the number $N$ of arms is very large, we
propose new algorithms in which each next arm is selected via an inner product
search. Such methods can be implemented via hashing algorithms (i.e.,
"hash-amenable") and result in a time complexity sublinear in $N$. While a
Thompson sampling extension of GLOC is hash-amenable, its regret bound for
$d$-dimensional arm sets scales with $d^{3/2}$, whereas GLOC's regret bound
scales with $d$. Towards closing this gap, we propose a new hash-amenable
algorithm whose regret bound scales with $d^{5/4}$. Finally, we propose a fast
approximate hash-key computation (inner product) with a better accuracy than
the state-of-the-art, which can be of independent interest. We conclude the
paper with preliminary experimental results confirming the merits of our
methods.

提出了新的可扩展算法来解决广义线性赌博机问题，基于在线计算的新算法（GLOC）将任何在线学习算法转化为 GLB 算法，同时，通过内积搜索，为选择大量臂的情况设计了新算法，并提出了一种快速准确的哈希键计算方法，并进行了实验验证。