Expressive Modeling Is Insufficient for Offline RL: A Tractable Inference Perspective

A popular paradigm for offline Reinforcement Learning (RL) tasks is to first fit the offline trajectories to a sequence model, and then prompt the model for actions that lead to high expected return. While a common consensus is that more expressive sequence models imply better performance, this paper highlights that tractability, the ability to exactly and efficiently answer various probabilistic queries, plays an equally important role. Specifically, due to the fundamental stochasticity from the offline data-collection policies and the environment dynamics, highly non-trivial conditional/constrained generation is required to elicit rewarding actions. While it is still possible to approximate such queries, we observe that such crude estimates significantly undermine the benefits brought by expressive sequence models. To overcome this problem, this paper proposes Trifle (Tractable Inference for Offline RL), which leverages modern Tractable Probabilistic Models (TPMs) to bridge the gap between good sequence models and high expected returns at evaluation time. Empirically, Trifle achieves the most state-of-the-art scores in 9 Gym-MuJoCo benchmarks against strong baselines. Further, owing to its tractability, Trifle significantly outperforms prior approaches in stochastic environments and safe RL tasks (e.g. with action constraints) with minimum algorithmic modifications.

Understanding the Distillation Process from Deep Generative Models to Tractable Probabilistic Circuits

Probabilistic Circuits (PCs) are a general and unified computational framework for tractable probabilistic models that support efficient computation of various inference tasks (e.g., computing marginal probabilities). Towards enabling such reasoning capabilities in complex real-world tasks, Liu et al. (2022) propose to distill knowledge (through latent variable assignments) from less tractable but more expressive deep generative models. However, it is still unclear what factors make this distillation work well. In this paper, we theoretically and empirically discover that the performance of a PC can exceed that of its teacher model. Therefore, instead of performing distillation from the most expressive deep generative model, we study what properties the teacher model and the PC should have in order to achieve good distillation performance. This leads to a generic algorithmic improvement as well as other data-type-specific ones over the existing latent variable distillation pipeline. Empirically, we outperform SoTA TPMs by a large margin on challenging image modeling benchmarks. In particular, on ImageNet32, PCs achieve 4.06 bits-per-dimension, which is only 0.34 behind variational diffusion models (Kingma et al., 2021).

Sparse Coding with Earth Mover's Distance for Multi-Instance Histogram Representation

Sparse coding (Sc) has been studied very well as a powerful data representation method. It attempts to represent the feature vector of a data sample by reconstructing it as the sparse linear combination of some basic elements, and a $L_2$ norm distance function is usually used as the loss function for the reconstruction error. In this paper, we investigate using Sc as the representation method within multi-instance learning framework, where a sample is given as a bag of instances, and further represented as a histogram of the quantized instances. We argue that for the data type of histogram, using $L_2$ norm distance is not suitable, and propose to use the earth mover's distance (EMD) instead of $L_2$ norm distance as a measure of the reconstruction error. By minimizing the EMD between the histogram of a sample and the its reconstruction from some basic histograms, a novel sparse coding method is developed, which is refereed as SC-EMD. We evaluate its performances as a histogram representation method in tow multi-instance learning problems --- abnormal image detection in wireless capsule endoscopy videos, and protein binding site retrieval. The encouraging results demonstrate the advantages of the new method over the traditional method using $L_2$ norm distance.

Supervised learning of sparse context reconstruction coefficients for data representation and classification

Context of data points, which is usually defined as the other data points in a data set, has been found to play important roles in data representation and classification. In this paper, we study the problem of using context of a data point for its classification problem. Our work is inspired by the observation that actually only very few data points are critical in the context of a data point for its representation and classification. We propose to represent a data point as the sparse linear combination of its context, and learn the sparse context in a supervised way to increase its discriminative ability. To this end, we proposed a novel formulation for context learning, by modeling the learning of context parameter and classifier in a unified objective, and optimizing it with an alternative strategy in an iterative algorithm. Experiments on three benchmark data set show its advantage over state-of-the-art context-based data representation and classification methods.