Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making

Decision-focused learning (DFL) integrates predictive models with downstream optimization, directly training machine learning models to minimize decision errors. While DFL has been shown to provide substantial advantages when compared to a counterpart that treats the predictive and prescriptive models separately, it has also been shown to struggle in high-dimensional and risk-sensitive settings, limiting its applicability in real-world settings. To address this limitation, this paper introduces decision-focused generative learning (Gen-DFL), a novel framework that leverages generative models to adaptively model uncertainty and improve decision quality. Instead of relying on fixed uncertainty sets, Gen-DFL learns a structured representation of the optimization parameters and samples from the tail regions of the learned distribution to enhance robustness against worst-case scenarios. This approach mitigates over-conservatism while capturing complex dependencies in the parameter space. The paper shows, theoretically, that Gen-DFL achieves improved worst-case performance bounds compared to traditional DFL. Empirically, it evaluates Gen-DFL on various scheduling and logistics problems, demonstrating its strong performance against existing DFL methods.

On the Encoder-Decoder Incompatibility in Variational Text Modeling and Beyond

Variational autoencoders (VAEs) combine latent variables with amortized variational inference, whose optimization usually converges into a trivial local optimum termed posterior collapse, especially in text modeling. By tracking the optimization dynamics, we observe the encoder-decoder incompatibility that leads to poor parameterizations of the data manifold. We argue that the trivial local optimum may be avoided by improving the encoder and decoder parameterizations since the posterior network is part of a transition map between them. To this end, we propose Coupled-VAE, which couples a VAE model with a deterministic autoencoder with the same structure and improves the encoder and decoder parameterizations via encoder weight sharing and decoder signal matching. We apply the proposed Coupled-VAE approach to various VAE models with different regularization, posterior family, decoder structure, and optimization strategy. Experiments on benchmark datasets (i.e., PTB, Yelp, and Yahoo) show consistently improved results in terms of probability estimation and richness of the latent space. We also generalize our method to conditional language modeling and propose Coupled-CVAE, which largely improves the diversity of dialogue generation on the Switchboard dataset.

Neural Gaussian Copula for Variational Autoencoder

Variational language models seek to estimate the posterior of latent variables with an approximated variational posterior. The model often assumes the variational posterior to be factorized even when the true posterior is not. The learned variational posterior under this assumption does not capture the dependency relationships over latent variables. We argue that this would cause a typical training problem called posterior collapse observed in all other variational language models. We propose Gaussian Copula Variational Autoencoder (VAE) to avert this problem. Copula is widely used to model correlation and dependencies of high-dimensional random variables, and therefore it is helpful to maintain the dependency relationships that are lost in VAE. The empirical results show that by modeling the correlation of latent variables explicitly using a neural parametric copula, we can avert this training difficulty while getting competitive results among all other VAE approaches.

Riemannian Normalizing Flow on Variational Wasserstein Autoencoder for Text Modeling

Recurrent Variational Autoencoder has been widely used for language modeling and text generation tasks. These models often face a difficult optimization problem, also known as the Kullback-Leibler (KL) term vanishing issue, where the posterior easily collapses to the prior, and the model will ignore latent codes in generative tasks. To address this problem, we introduce an improved Wasserstein Variational Autoencoder (WAE) with Riemannian Normalizing Flow (RNF) for text modeling. The RNF transforms a latent variable into a space that respects the geometric characteristics of input space, which makes posterior impossible to collapse to the non-informative prior. The Wasserstein objective minimizes the distance between the marginal distribution and the prior directly and therefore does not force the posterior to match the prior. Empirical experiments show that our model avoids KL vanishing over a range of datasets and has better performances in tasks such as language modeling, likelihood approximation, and text generation. Through a series of experiments and analysis over latent space, we show that our model learns latent distributions that respect latent space geometry and is able to generate sentences that are more diverse.