The Machine Learning for Combinatorial Optimization (ML4CO) NeurIPS 2021 competition aims to improve state-of-the-art combinatorial optimization solvers by replacing key heuristic components with machine learning models. On the dual task, we design models to make branching decisions to promote the dual bound increase faster. We propose a knowledge inheritance method to generalize knowledge of different models from the dataset aggregation process, named KIDA. Our improvement overcomes some defects of the baseline graph-neural-networks-based methods. Further, we won the $1$\textsuperscript{st} Place on the dual task. We hope this report can provide useful experience for developers and researchers. The code is available at https://github.com/megvii-research/NeurIPS2021-ML4CO-KIDA.

Clustering points in a vector space or nodes in a graph is a ubiquitous primitive in statistical data analysis, and it is commonly used for exploratory data analysis. In practice, it is often of interest to "refine" or "improve" a given cluster that has been obtained by some other method. In this survey, we focus on principled algorithms for this cluster improvement problem. Many such cluster improvement algorithms are flow-based methods, by which we mean that operationally they require the solution of a sequence of maximum flow problems on a (typically implicitly) modified data graph. These cluster improvement algorithms are powerful, both in theory and in practice, but they have not been widely adopted for problems such as community detection, local graph clustering, semi-supervised learning, etc. Possible reasons for this are: the steep learning curve for these algorithms; the lack of efficient and easy to use software; and the lack of detailed numerical experiments on real-world data that demonstrate their usefulness. Our objective here is to address these issues. To do so, we guide the reader through the whole process of understanding how to implement and apply these powerful algorithms. We present a unifying fractional programming optimization framework that permits us to distill, in a simple way, the crucial components of all these algorithms. It also makes apparent similarities and differences between related methods. Viewing these cluster improvement algorithms via a fractional programming framework suggests directions for future algorithm development. Finally, we develop efficient implementations of these algorithms in our LocalGraphClustering Python package, and we perform extensive numerical experiments to demonstrate the performance of these methods on social networks and image-based data graphs.

In this manuscript, we offer a gentle review of submodularity and supermodularity and their properties. We offer a plethora of submodular definitions; a full description of a number of example submodular functions and their generalizations; example discrete constraints; a discussion of basic algorithms for maximization, minimization, and other operations; a brief overview of continuous submodular extensions; and some historical applications. We then turn to how submodularity is useful in machine learning and artificial intelligence. This includes summarization, and we offer a complete account of the differences between and commonalities amongst sketching, coresets, extractive and abstractive summarization in NLP, data distillation and condensation, and data subset selection and feature selection. We discuss a variety of ways to produce a submodular function useful for machine learning, including heuristic hand-crafting, learning or approximately learning a submodular function or aspects thereof, and some advantages of the use of a submodular function as a coreset producer. We discuss submodular combinatorial information functions, and how submodularity is useful for clustering, data partitioning, parallel machine learning, active and semi-supervised learning, probabilistic modeling, and structured norms and loss functions.

Team GB bobsleigh pilot Brad Hall tries to complete a Rubik's cube faster than a bobsleigh run.

The classical Policy Iteration (PI) algorithm alternates between greedy one-step policy improvement and policy evaluation. Recent literature shows that multi-step lookahead policy improvement leads to a better convergence rate at the expense of increased complexity per iteration. However, prior to running the algorithm, one cannot tell what is the best fixed lookahead horizon. Moreover, per a given run, using a lookahead of horizon larger than one is often wasteful. In this work, we propose for the first time to dynamically adapt the multi-step lookahead horizon as a function of the state and of the value estimate. We devise two PI variants and analyze the trade-off between iteration count and computational complexity per iteration. The first variant takes the desired contraction factor as the objective and minimizes the per-iteration complexity. The second variant takes as input the computational complexity per iteration and minimizes the overall contraction factor. We then devise a corresponding DQN-based algorithm with an adaptive tree search horizon. We also include a novel enhancement for on-policy learning: per-depth value function estimator. Lastly, we demonstrate the efficacy of our adaptive lookahead method in a maze environment and in Atari.

In feature-based dynamic pricing, a seller sets appropriate prices for a sequence of products (described by feature vectors) on the fly by learning from the binary outcomes of previous sales sessions ("Sold" if valuation $\geq$ price, and "Not Sold" otherwise). Existing works either assume noiseless linear valuation or precisely-known noise distribution, which limits the applicability of those algorithms in practice when these assumptions are hard to verify. In this work, we study two more agnostic models: (a) a "linear policy" problem where we aim at competing with the best linear pricing policy while making no assumptions on the data, and (b) a "linear noisy valuation" problem where the random valuation is linear plus an unknown and assumption-free noise. For the former model, we show a $\tilde{\Theta}(d^{\frac13}T^{\frac23})$ minimax regret up to logarithmic factors. For the latter model, we present an algorithm that achieves an $\tilde{O}(T^{\frac34})$ regret, and improve the best-known lower bound from $\Omega(T^{\frac35})$ to $\tilde{\Omega}(T^{\frac23})$. These results demonstrate that no-regret learning is possible for feature-based dynamic pricing under weak assumptions, but also reveal a disappointing fact that the seemingly richer pricing feedback is not significantly more useful than the bandit-feedback in regret reduction.

Dataflow/mapping decides the compute and energy efficiency of DNN accelerators. Many mappers have been proposed to tackle the intra-layer map-space. However, mappers for inter-layer map-space (aka layer-fusion map-space), have been rarely discussed. In this work, we propose a mapper, DNNFuser, specifically focusing on this layer-fusion map-space. While existing SOTA DNN mapping explorations rely on search-based mappers, this is the first work, to the best of our knowledge, to propose a one-shot inference-based mapper. We leverage a famous language model GPT as our DNN architecture to learn layer-fusion optimization as a sequence modeling problem. Further, the trained DNNFuser can generalize its knowledge and infer new solutions for unseen conditions. Within one inference pass, DNNFuser can infer solutions with compatible performance to the ones found by a highly optimized search-based mapper while being 66x-127x faster.

This paper presents an empirical investigation of the relation between decision speed and decision quality for a real-world setting of cognitively-demanding decisions in which the timing of decisions is endogenous: professional chess. Move-by-move data provide exceptionally detailed and precise information about decision times and decision quality, based on a comparison of actual decisions to a computational benchmark of best moves constructed using the artificial intelligence of a chess engine. The results reveal that faster decisions are associated with better performance. The findings are consistent with the predictions of procedural decision models like drift-diffusion-models in which decision makers sequentially acquire information about decision alternatives with uncertain valuations.

Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by learning the problem-specific solution structure. However, reproducing the results of these publications proves to be difficult. We make three contributions. First, we present an open-source benchmark suite for the NP-hard Maximum Independent Set problem, in both its weighted and unweighted variants. The suite offers a unified interface to various state-of-the-art traditional and machine learning-based solvers. Second, using our benchmark suite, we conduct an in-depth analysis of the popular guided tree search algorithm by Li et al. [NeurIPS 2018], testing various configurations on small and large synthetic and real-world graphs. By re-implementing their algorithm with a focus on code quality and extensibility, we show that the graph convolution network used in the tree search does not learn a meaningful representation of the solution structure, and can in fact be replaced by random values. Instead, the tree search relies on algorithmic techniques like graph kernelization to find good solutions. Thus, the results from the original publication are not reproducible. Third, we extend the analysis to compare the tree search implementations to other solvers, showing that the classical algorithmic solvers often are faster, while providing solutions of similar quality. Additionally, we analyze a recent solver based on reinforcement learning and observe that for this solver, the GNN is responsible for the competitive solution quality.

With increasing interest in procedural content generation by academia and game developers alike, it is vital that different approaches can be compared fairly. However, evaluating procedurally generated video game levels is often difficult, due to the lack of standardised, game-independent metrics. In this paper, we introduce two simulation-based evaluation metrics that involve analysing the behaviour of an A* agent to measure the diversity and difficulty of generated levels in a general, game-independent manner. Diversity is calculated by comparing action trajectories from different levels using the edit distance, and difficulty is measured as how much exploration and expansion of the A* search tree is necessary before the agent can solve the level. We demonstrate that our diversity metric is more robust to changes in level size and representation than current methods and additionally measures factors that directly affect playability, instead of focusing on visual information. The difficulty metric shows promise, as it correlates with existing estimates of difficulty in one of the tested domains, but it does face some challenges in the other domain. Finally, to promote reproducibility, we publicly release our evaluation framework.