4 research outputs found
Revisiting Projection-Free Optimization for Strongly Convex Constraint Sets
We revisit the Frank-Wolfe (FW) optimization under strongly convex constraint
sets. We provide a faster convergence rate for FW without line search, showing
that a previously overlooked variant of FW is indeed faster than the standard
variant. With line search, we show that FW can converge to the global optimum,
even for smooth functions that are not convex, but are quasi-convex and
locally-Lipschitz. We also show that, for the general case of (smooth)
non-convex functions, FW with line search converges with high probability to a
stationary point at a rate of , as long as the
constraint set is strongly convex -- one of the fastest convergence rates in
non-convex optimization.Comment: Extended version of paper accepted at AAAI-19, 19 pages, 10 figure
Multi-Objective GFlowNets
We study the problem of generating diverse candidates in the context of
Multi-Objective Optimization. In many applications of machine learning such as
drug discovery and material design, the goal is to generate candidates which
simultaneously optimize a set of potentially conflicting objectives. Moreover,
these objectives are often imperfect evaluations of some underlying property of
interest, making it important to generate diverse candidates to have multiple
options for expensive downstream evaluations. We propose Multi-Objective
GFlowNets (MOGFNs), a novel method for generating diverse Pareto optimal
solutions, based on GFlowNets. We introduce two variants of MOGFNs: MOGFN-PC,
which models a family of independent sub-problems defined by a scalarization
function, with reward-conditional GFlowNets, and MOGFN-AL, which solves a
sequence of sub-problems defined by an acquisition function in an active
learning loop. Our experiments on wide variety of synthetic and benchmark tasks
demonstrate advantages of the proposed methods in terms of the Pareto
performance and importantly, improved candidate diversity, which is the main
contribution of this work.Comment: 23 pages, 8 figures. ICML 2023. Code at:
https://github.com/GFNOrg/multi-objective-gf
Improving and generalizing flow-based generative models with minibatch optimal transport
Continuous normalizing flows (CNFs) are an attractive generative modeling
technique, but they have been held back by limitations in their
simulation-based maximum likelihood training. We introduce the generalized
conditional flow matching (CFM) technique, a family of simulation-free training
objectives for CNFs. CFM features a stable regression objective like that used
to train the stochastic flow in diffusion models but enjoys the efficient
inference of deterministic flow models. In contrast to both diffusion models
and prior CNF training algorithms, CFM does not require the source distribution
to be Gaussian or require evaluation of its density. A variant of our objective
is optimal transport CFM (OT-CFM), which creates simpler flows that are more
stable to train and lead to faster inference, as evaluated in our experiments.
Furthermore, OT-CFM is the first method to compute dynamic OT in a
simulation-free way. Training CNFs with CFM improves results on a variety of
conditional and unconditional generation tasks, such as inferring single cell
dynamics, unsupervised image translation, and Schr\"odinger bridge inference.Comment: A version of this paper appeared in the New Frontiers in Learning,
Control, and Dynamical Systems workshop at ICML 2023. Title change from v1.
Code: https://github.com/atong01/conditional-flow-matchin
Learning GFlowNets from partial episodes for improved convergence and stability
Generative flow networks (GFlowNets) are a family of algorithms for training
a sequential sampler of discrete objects under an unnormalized target density
and have been successfully used for various probabilistic modeling tasks.
Existing training objectives for GFlowNets are either local to states or
transitions, or propagate a reward signal over an entire sampling trajectory.
We argue that these alternatives represent opposite ends of a gradient
bias-variance tradeoff and propose a way to exploit this tradeoff to mitigate
its harmful effects. Inspired by the TD() algorithm in reinforcement
learning, we introduce subtrajectory balance or SubTB(), a GFlowNet
training objective that can learn from partial action subsequences of varying
lengths. We show that SubTB() accelerates sampler convergence in
previously studied and new environments and enables training GFlowNets in
environments with longer action sequences and sparser reward landscapes than
what was possible before. We also perform a comparative analysis of stochastic
gradient dynamics, shedding light on the bias-variance tradeoff in GFlowNet
training and the advantages of subtrajectory balance.Comment: ICML 202