Recently, deep reinforcement learning (DRL) models have shown promising results in solving NP-hard Combinatorial Optimization (CO) problems. However, most DRL solvers can only scale to a few hundreds of nodes for combinatorial optimization problems on graphs, such as the Traveling Salesman Problem (TSP). This paper addresses the scalability challenge in large-scale combinatorial optimization by proposing a novel approach, namely, DIMES. Unlike previous DRL methods which suffer from costly autoregressive decoding or iterative refinements of discrete solutions, DIMES introduces a compact continuous space for parameterizing the underlying distribution of candidate solutions. Such a continuous space allows stable REINFORCE-based training and fine-tuning via massively parallel sampling. We further propose a meta-learning framework to enable the effective initialization of model parameters in the fine-tuning stage. Extensive experiments show that DIMES outperforms recent DRL-based methods on large benchmark datasets for Traveling Salesman Problems and Maximal Independent Set problems.
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Given ample experimental data from a system governed by differential equations, it is possible to use deep learning techniques to construct the underlying differential operators. In this work we perform symbolic discovery of differential operators in a situation where there is sparse experimental data. This small data regime in machine learning can be made tractable by providing our algorithms with prior information about the underlying dynamics. Physics Informed Neural Networks (PINNs) have been very successful in this regime (reconstructing entire ODE solutions using only a single point or entire PDE solutions with very few measurements of the initial condition). We modify the PINN approach by adding a neural network that learns a representation of unknown hidden terms in the differential equation. The algorithm yields both a surrogate solution to the differential equation and a black-box representation of the hidden terms. These hidden term neural networks can then be converted into symbolic equations using symbolic regression techniques like AI Feynman. In order to achieve convergence of these neural networks, we provide our algorithms with (noisy) measurements of both the initial condition as well as (synthetic) experimental data obtained at later times. We demonstrate strong performance of this approach even when provided with very few measurements of noisy data in both the ODE and PDE regime.
Conditional normalizing flows can generate diverse image samples for solving inverse problems. Most normalizing flows for inverse problems in imaging employ the conditional affine coupling layer that can generate diverse images quickly. However, unintended severe artifacts are occasionally observed in the output of them. In this work, we address this critical issue by investigating the origins of these artifacts and proposing the conditions to avoid them. First of all, we empirically and theoretically reveal that these problems are caused by ``exploding variance'' in the conditional affine coupling layer for certain out-of-distribution (OOD) conditional inputs. Then, we further validated that the probability of causing erroneous artifacts in pixels is highly correlated with a Mahalanobis distance-based OOD score for inverse problems in imaging. Lastly, based on our investigations, we propose a remark to avoid exploding variance and then based on it, we suggest a simple remedy that substitutes the affine coupling layers with the modified rational quadratic spline coupling layers in normalizing flows, to encourage the robustness of generated image samples. Our experimental results demonstrated that our suggested methods effectively suppressed critical artifacts occurring in normalizing flows for super-resolution space generation and low-light image enhancement without compromising performance.
Traditional power grid systems have become obsolete under more frequent and extreme natural disasters. Reinforcement learning (RL) has been a promising solution for resilience given its successful history of power grid control. However, most power grid simulators and RL interfaces do not support simulation of power grid under large-scale blackouts or when the network is divided into sub-networks. In this study, we proposed an updated power grid simulator built on Grid2Op, an existing simulator and RL interface, and experimented on limiting the action and observation spaces of Grid2Op. By testing with DDQN and SliceRDQN algorithms, we found that reduced action spaces significantly improve training performance and efficiency. In addition, we investigated a low-rank neural network regularization method for deep Q-learning, one of the most widely used RL algorithms, in this power grid control scenario. As a result, the experiment demonstrated that in the power grid simulation environment, adopting this method will significantly increase the performance of RL agents.
Recent advances of data-driven machine learning have revolutionized fields like computer vision, reinforcement learning, and many scientific and engineering domains. In many real-world and scientific problems, systems that generate data are governed by physical laws. Recent work shows that it provides potential benefits for machine learning models by incorporating the physical prior and collected data, which makes the intersection of machine learning and physics become a prevailing paradigm. In this survey, we present this learning paradigm called Physics-Informed Machine Learning (PIML) which is to build a model that leverages empirical data and available physical prior knowledge to improve performance on a set of tasks that involve a physical mechanism. We systematically review the recent development of physics-informed machine learning from three perspectives of machine learning tasks, representation of physical prior, and methods for incorporating physical prior. We also propose several important open research problems based on the current trends in the field. We argue that encoding different forms of physical prior into model architectures, optimizers, inference algorithms, and significant domain-specific applications like inverse engineering design and robotic control is far from fully being explored in the field of physics-informed machine learning. We believe that this study will encourage researchers in the machine learning community to actively participate in the interdisciplinary research of physics-informed machine learning.
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.
Recommender systems have been widely applied in different real-life scenarios to help us find useful information. Recently, Reinforcement Learning (RL) based recommender systems have become an emerging research topic. It often surpasses traditional recommendation models even most deep learning-based methods, owing to its interactive nature and autonomous learning ability. Nevertheless, there are various challenges of RL when applying in recommender systems. Toward this end, we firstly provide a thorough overview, comparisons, and summarization of RL approaches for five typical recommendation scenarios, following three main categories of RL: value-function, policy search, and Actor-Critic. Then, we systematically analyze the challenges and relevant solutions on the basis of existing literature. Finally, under discussion for open issues of RL and its limitations of recommendation, we highlight some potential research directions in this field.
Bid optimization for online advertising from single advertiser's perspective has been thoroughly investigated in both academic research and industrial practice. However, existing work typically assume competitors do not change their bids, i.e., the wining price is fixed, leading to poor performance of the derived solution. Although a few studies use multi-agent reinforcement learning to set up a cooperative game, they still suffer the following drawbacks: (1) They fail to avoid collusion solutions where all the advertisers involved in an auction collude to bid an extremely low price on purpose. (2) Previous works cannot well handle the underlying complex bidding environment, leading to poor model convergence. This problem could be amplified when handling multiple objectives of advertisers which are practical demands but not considered by previous work. In this paper, we propose a novel multi-objective cooperative bid optimization formulation called Multi-Agent Cooperative bidding Games (MACG). MACG sets up a carefully designed multi-objective optimization framework where different objectives of advertisers are incorporated. A global objective to maximize the overall profit of all advertisements is added in order to encourage better cooperation and also to protect self-bidding advertisers. To avoid collusion, we also introduce an extra platform revenue constraint. We analyze the optimal functional form of the bidding formula theoretically and design a policy network accordingly to generate auction-level bids. Then we design an efficient multi-agent evolutionary strategy for model optimization. Offline experiments and online A/B tests conducted on the Taobao platform indicate both single advertiser's objective and global profit have been significantly improved compared to state-of-art methods.
Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
Recommender System (RS) is a hot area where artificial intelligence (AI) techniques can be effectively applied to improve performance. Since the well-known Netflix Challenge, collaborative filtering (CF) has become the most popular and effective recommendation method. Despite their success in CF, various AI techniques still have to face the data sparsity and cold start problems. Previous works tried to solve these two problems by utilizing auxiliary information, such as social connections among users and meta-data of items. However, they process different types of information separately, leading to information loss. In this work, we propose to utilize Heterogeneous Information Network (HIN), which is a natural and general representation of different types of data, to enhance CF-based recommending methods. HIN-based recommender systems face two problems: how to represent high-level semantics for recommendation and how to fuse the heterogeneous information to recommend. To address these problems, we propose to applying meta-graph to HIN-based RS and solve the information fusion problem with a "matrix factorization (MF) + factorization machine (FM)" framework. For the "MF" part, we obtain user-item similarity matrices from each meta-graph and adopt low-rank matrix approximation to get latent features for both users and items. For the "FM" part, we propose to apply FM with Group lasso (FMG) on the obtained features to simultaneously predict missing ratings and select useful meta-graphs. Experimental results on two large real-world datasets, i.e., Amazon and Yelp, show that our proposed approach is better than that of the state-of-the-art FM and other HIN-based recommending methods.
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