2,120 research outputs found
On Graduated Optimization for Stochastic Non-Convex Problems
The graduated optimization approach, also known as the continuation method,
is a popular heuristic to solving non-convex problems that has received renewed
interest over the last decade. Despite its popularity, very little is known in
terms of theoretical convergence analysis. In this paper we describe a new
first-order algorithm based on graduated optimiza- tion and analyze its
performance. We characterize a parameterized family of non- convex functions
for which this algorithm provably converges to a global optimum. In particular,
we prove that the algorithm converges to an {\epsilon}-approximate solution
within O(1/\epsilon^2) gradient-based steps. We extend our algorithm and
analysis to the setting of stochastic non-convex optimization with noisy
gradient feedback, attaining the same convergence rate. Additionally, we
discuss the setting of zero-order optimization, and devise a a variant of our
algorithm which converges at rate of O(d^2/\epsilon^4).Comment: 17 page
Deep metric learning to rank
We propose a novel deep metric learning method by revisiting the learning to rank approach. Our method, named FastAP, optimizes the rank-based Average Precision measure, using an approximation derived from distance quantization. FastAP has a low complexity compared to existing methods, and is tailored for stochastic gradient descent. To fully exploit the benefits of the ranking formulation, we also propose a new minibatch sampling scheme, as well as a simple heuristic to enable large-batch training. On three few-shot image retrieval datasets, FastAP consistently outperforms competing methods, which often involve complex optimization heuristics or costly model ensembles.Accepted manuscrip
LambdaFM: Learning Optimal Ranking with Factorization Machines Using Lambda Surrogates
State-of-the-art item recommendation algorithms, which apply
Factorization Machines (FM) as a scoring function and
pairwise ranking loss as a trainer (PRFM for short), have
been recently investigated for the implicit feedback based
context-aware recommendation problem (IFCAR). However,
good recommenders particularly emphasize on the accuracy
near the top of the ranked list, and typical pairwise loss functions
might not match well with such a requirement. In this
paper, we demonstrate, both theoretically and empirically,
PRFM models usually lead to non-optimal item recommendation
results due to such a mismatch. Inspired by the success
of LambdaRank, we introduce Lambda Factorization
Machines (LambdaFM), which is particularly intended for
optimizing ranking performance for IFCAR. We also point
out that the original lambda function suffers from the issue
of expensive computational complexity in such settings due
to a large amount of unobserved feedback. Hence, instead
of directly adopting the original lambda strategy, we create
three effective lambda surrogates by conducting a theoretical
analysis for lambda from the top-N optimization perspective.
Further, we prove that the proposed lambda surrogates
are generic and applicable to a large set of pairwise
ranking loss functions. Experimental results demonstrate
LambdaFM significantly outperforms state-of-the-art algorithms
on three real-world datasets in terms of four standard
ranking measures
- …