Revisiting the Characteristics of Stochastic Gradient Noise and Dynamics

In this paper, we characterize the noise of stochastic gradients and analyze the noise-induced dynamics during training deep neural networks by gradient-based optimizers. Specifically, we firstly show that the stochastic gradient noise possesses finite variance, and therefore the classical Central Limit Theorem (CLT) applies; this indicates that the gradient noise is asymptotically Gaussian. Such an asymptotic result validates the wide-accepted assumption of Gaussian noise. We clarify that the recently observed phenomenon of heavy tails within gradient noise may not be intrinsic properties, but the consequence of insufficient mini-batch size; the gradient noise, which is a sum of limited i.i.d. random variables, has not reached the asymptotic regime of CLT, thus deviates from Gaussian. We quantitatively measure the goodness of Gaussian approximation of the noise, which supports our conclusion. Secondly, we analyze the noise-induced dynamics of stochastic gradient descent using the Langevin equation, granting for momentum hyperparameter in the optimizer with a physical interpretation. We then proceed to demonstrate the existence of the steady-state distribution of stochastic gradient descent and approximate the distribution at a small learning rate.

Top-N Recommendation with Counterfactual User Preference Simulation

Top-N recommendation, which aims to learn user ranking-based preference, has long been a fundamental problem in a wide range of applications. Traditional models usually motivate themselves by designing complex or tailored architectures based on different assumptions. However, the training data of recommender system can be extremely sparse and imbalanced, which poses great challenges for boosting the recommendation performance. To alleviate this problem, in this paper, we propose to reformulate the recommendation task within the causal inference framework, which enables us to counterfactually simulate user ranking-based preferences to handle the data scarce problem. The core of our model lies in the counterfactual question: "what would be the user's decision if the recommended items had been different?". To answer this question, we firstly formulate the recommendation process with a series of structural equation models (SEMs), whose parameters are optimized based on the observed data. Then, we actively indicate many recommendation lists (called intervention in the causal inference terminology) which are not recorded in the dataset, and simulate user feedback according to the learned SEMs for generating new training samples. Instead of randomly intervening on the recommendation list, we design a learning-based method to discover more informative training samples. Considering that the learned SEMs can be not perfect, we, at last, theoretically analyze the relation between the number of generated samples and the model prediction error, based on which a heuristic method is designed to control the negative effect brought by the prediction error. Extensive experiments are conducted based on both synthetic and real-world datasets to demonstrate the effectiveness of our framework.

Recommendation Fairness: From Static to Dynamic

Driven by the need to capture users' evolving interests and optimize their long-term experiences, more and more recommender systems have started to model recommendation as a Markov decision process and employ reinforcement learning to address the problem. Shouldn't research on the fairness of recommender systems follow the same trend from static evaluation and one-shot intervention to dynamic monitoring and non-stop control? In this paper, we portray the recent developments in recommender systems first and then discuss how fairness could be baked into the reinforcement learning techniques for recommendation. Moreover, we argue that in order to make further progress in recommendation fairness, we may want to consider multi-agent (game-theoretic) optimization, multi-objective (Pareto) optimization, and simulation-based optimization, in the general framework of stochastic games.

CMML: Contextual Modulation Meta Learning for Cold-Start Recommendation

Practical recommender systems experience a cold-start problem when observed user-item interactions in the history are insufficient. Meta learning, especially gradient based one, can be adopted to tackle this problem by learning initial parameters of the model and thus allowing fast adaptation to a specific task from limited data examples. Though with significant performance improvement, it commonly suffers from two critical issues: the non-compatibility with mainstream industrial deployment and the heavy computational burdens, both due to the inner-loop gradient operation. These two issues make them hard to be applied in practical recommender systems. To enjoy the benefits of meta learning framework and mitigate these problems, we propose a recommendation framework called Contextual Modulation Meta Learning (CMML). CMML is composed of fully feed-forward operations so it is computationally efficient and completely compatible with the mainstream industrial deployment. CMML consists of three components, including a context encoder that can generate context embedding to represent a specific task, a hybrid context generator that aggregates specific user-item features with task-level context, and a contextual modulation network, which can modulate the recommendation model to adapt effectively. We validate our approach on both scenario-specific and user-specific cold-start setting on various real-world datasets, showing CMML can achieve comparable or even better performance with gradient based methods yet with much higher computational efficiency and better interpretability.

On the Complexity of Computing Markov Perfect Equilibrium in General-Sum Stochastic Games

Similar to the role of Markov decision processes in reinforcement learning, Stochastic Games (SGs) lay the foundation for the study of multi-agent reinforcement learning (MARL) and sequential agent interactions. In this paper, we derive that computing an approximate Markov Perfect Equilibrium (MPE) in a finite-state discounted Stochastic Game within the exponential precision is \textbf{PPAD}-complete. We adopt a function with a polynomially bounded description in the strategy space to convert the MPE computation to a fixed-point problem, even though the stochastic game may demand an exponential number of pure strategies, in the number of states, for each agent. The completeness result follows the reduction of the fixed-point problem to {\sc End of the Line}. Our results indicate that finding an MPE in SGs is highly unlikely to be \textbf{NP}-hard unless \textbf{NP}=\textbf{co-NP}. Our work offers confidence for MARL research to study MPE computation on general-sum SGs and to develop fruitful algorithms as currently on zero-sum SGs.

Bilateral Denoising Diffusion Models

Denoising diffusion probabilistic models (DDPMs) have emerged as competitive generative models yet brought challenges to efficient sampling. In this paper, we propose novel bilateral denoising diffusion models (BDDMs), which take significantly fewer steps to generate high-quality samples. From a bilateral modeling objective, BDDMs parameterize the forward and reverse processes with a score network and a scheduling network, respectively. We show that a new lower bound tighter than the standard evidence lower bound can be derived as a surrogate objective for training the two networks. In particular, BDDMs are efficient, simple-to-train, and capable of further improving any pre-trained DDPM by optimizing the inference noise schedules. Our experiments demonstrated that BDDMs can generate high-fidelity samples with as few as 3 sampling steps and produce comparable or even higher quality samples than DDPMs using 1000 steps with only 16 sampling steps (a 62x speedup).