Alpha Elimination: Using Deep Reinforcement Learning to Reduce Fill-In during Sparse Matrix Decomposition

A large number of computational and scientific methods commonly require decomposing a sparse matrix into triangular factors as LU decomposition. A common problem faced during this decomposition is that even though the given matrix may be very sparse, the decomposition may lead to a denser triangular factors due to fill-in. A significant fill-in may lead to prohibitively larger computational costs and memory requirement during decomposition as well as during the solve phase. To this end, several heuristic sparse matrix reordering methods have been proposed to reduce fill-in before the decomposition. However, finding an optimal reordering algorithm that leads to minimal fill-in during such decomposition is known to be a NP-hard problem. A reinforcement learning based approach is proposed for this problem. The sparse matrix reordering problem is formulated as a single player game. More specifically, Monte-Carlo tree search in combination with neural network is used as a decision making algorithm to search for the best move in our game. The proposed method, alphaElimination is found to produce significantly lesser non-zeros in the LU decomposition as compared to existing state-of-the-art heuristic algorithms with little to no increase in overall running time of the algorithm. The code for the project will be publicly available here\footnote{\url{https://github.com/misterpawan/alphaEliminationPaper}}.

Explaining RL Decisions with Trajectories

Explanation is a key component for the adoption of reinforcement learning (RL) in many real-world decision-making problems. In the literature, the explanation is often provided by saliency attribution to the features of the RL agent's state. In this work, we propose a complementary approach to these explanations, particularly for offline RL, where we attribute the policy decisions of a trained RL agent to the trajectories encountered by it during training. To do so, we encode trajectories in offline training data individually as well as collectively (encoding a set of trajectories). We then attribute policy decisions to a set of trajectories in this encoded space by estimating the sensitivity of the decision with respect to that set. Further, we demonstrate the effectiveness of the proposed approach in terms of quality of attributions as well as practical scalability in diverse environments that involve both discrete and continuous state and action spaces such as grid-worlds, video games (Atari) and continuous control (MuJoCo). We also conduct a human study on a simple navigation task to observe how their understanding of the task compares with data attributed for a trained RL policy. Keywords -- Explainable AI, Verifiability of AI Decisions, Explainable RL.

Light-weight Deep Extreme Multilabel Classification

Extreme multi-label (XML) classification refers to the task of supervised multi-label learning that involves a large number of labels. Hence, scalability of the classifier with increasing label dimension is an important consideration. In this paper, we develop a method called LightDXML which modifies the recently developed deep learning based XML framework by using label embeddings instead of feature embedding for negative sampling and iterating cyclically through three major phases: (1) proxy training of label embeddings (2) shortlisting of labels for negative sampling and (3) final classifier training using the negative samples. Consequently, LightDXML also removes the requirement of a re-ranker module, thereby, leading to further savings on time and memory requirements. The proposed method achieves the best of both worlds: while the training time, model size and prediction times are on par or better compared to the tree-based methods, it attains much better prediction accuracy that is on par with the deep learning based methods. Moreover, the proposed approach achieves the best tail-label prediction accuracy over most state-of-the-art XML methods on some of the large datasets\footnote{accepted in IJCNN 2023, partial funding from MAPG grant and IIIT Seed grant at IIIT, Hyderabad, India. Code: \url{https://github.com/misterpawan/LightDXML}

Review of Extreme Multilabel Classification

Extreme multilabel classification or XML, in short, has emerged as a new subtopic of interest in machine learning. Compared to traditional multilabel classification, here the number of labels is extremely large, hence the name extreme multilabel classification. Using classical one versus all classification wont scale in this case due to large number of labels, same is true for any other classifiers. Embedding of labels as well as features into smaller label space is an essential first step. Moreover, other issues include existance of head and tail labels, where tail labels are labels which exist in relatively smaller number of given samples. The existence of tail labels creates issues during embedding. This area has invited application of wide range of approaches ranging from bit compression motivated from compressed sensing, tree based embeddings, deep learning based latent space embedding including using attention weights, linear algebra based embeddings such as SVD, clustering, hashing, to name a few. The community has come up with a useful set of metrics to identify the correctly the prediction for head or tail labels.