Cutting planes (cuts) are essential for solving mixed-integer linear programming (MILP) problems, as they tighten the feasible solution space and accelerate the solving process. Modern MILP solvers offer diverse cutting plane separators to generate cuts, enabling users to leverage their potential complementary strengths to tackle problems with different structures. Recent machine learning approaches learn to configure separators based on problem-specific features, selecting effective separators and deactivating ineffective ones to save unnecessary computing time. However, they ignore the dynamics of separator efficacy at different stages of cut generation and struggle to adapt the configurations for the evolving problems after multiple rounds of cut generation. To address this challenge, we propose a novel **dyn**amic **sep**arator configuration (**DynSep**) method that models separator configuration in different rounds as a reinforcement learning task, making decisions based on an incremental triplet graph updated by iteratively added cuts. Specifically, we tokenize the incremental subgraphs and utilize a decoder-only Transformer as our policy to autoregressively predict when to halt separation and which separators to activate at each round. Evaluated on synthetic and large-scale real-world MILP problems, DynSep speeds up average solving time by 64% on easy and medium datasets, and reduces primal-dual gap integral within the given time limit by 16% on hard datasets. Moreover, experiments demonstrate that DynSep well generalizes to MILP instances of significantly larger sizes than those seen during training.

Sample efficiency remains a key challenge for the deployment of deep reinforcement learning (RL) in real-world scenarios. A common approach is to learn efficient representations through future prediction tasks, facilitating the agent to make farsighted decisions that benefit its long-term performance. Existing methods extract predictive features by predicting multi-step future state signals. However, they do not fully exploit the structural information inherent in sequential state signals, which can potentially improve the quality of long-term decision-making but is difficult to discern in the time domain. To tackle this problem, we introduce a new perspective that leverages the frequency domain of state sequences to extract the underlying patterns in time series data. We theoretically show that state sequences contain structural information closely tied to policy performance and signal regularity and analyze the fitness of the frequency domain for extracting these two types of structural information. Inspired by that, we propose a novel representation learning method, State Sequences Prediction via Fourier Transform (SPF), which extracts long-term features by predicting the Fourier transform of infinite-step future state sequences. The appealing features of our frequency prediction objective include: 1) simple to implement due to a recursive relationship; 2) providing an upper bound on the performance difference between the optimal policy and the latent policy in the representation space. Experiments on standard and goal-conditioned RL tasks demonstrate that the proposed method outperforms several state-of-the-art algorithms in terms of both sample efficiency and performance.

While deep reinforcement learning (RL) has been demonstrated effective in solving complex control tasks, sample efficiency remains a key challenge due to the large amounts of data required for remarkable performance. Existing research explores the application of representation learning for data-efficient RL, e.g., learning predictive representations by predicting long-term future states. However, many existing methods do not fully exploit the structural information inherent in sequential state signals, which can potentially improve the quality of long-term decision-making but is difficult to discern in the time domain. To tackle this problem, we propose State Sequences Prediction via Fourier Transform (SPF), a novel method that exploits the frequency domain of state sequences to extract the underlying patterns in time series data for learning expressive representations efficiently. Specifically, we theoretically analyze the existence of structural information in state sequences, which is closely related to policy performance and signal regularity, and then propose to predict the Fourier transform of infinite-step future state sequences to extract such information. One of the appealing features of SPF is that it is simple to implement while not requiring storage of infinite-step future states as prediction targets. Experiments demonstrate that the proposed method outperforms several state-of-the-art algorithms in terms of both sample efficiency and performance.

Generalization across different environments with the same tasks is critical for successful applications of visual reinforcement learning (RL) in real scenarios. However, visual distractions---which are common in real scenes---from high-dimensional observations can be hurtful to the learned representations in visual RL, thus degrading the performance of generalization. To tackle this problem, we propose a novel approach, namely Characteristic Reward Sequence Prediction (CRESP), to extract the task-relevant information by learning reward sequence distributions (RSDs), as the reward signals are task-relevant in RL and invariant to visual distractions. Specifically, to effectively capture the task-relevant information via RSDs, CRESP introduces an auxiliary task---that is, predicting the characteristic functions of RSDs---to learn task-relevant representations, because we can well approximate the high-dimensional distributions by leveraging the corresponding characteristic functions. Experiments demonstrate that CRESP significantly improves the performance of generalization on unseen environments, outperforming several state-of-the-arts on DeepMind Control tasks with different visual distractions.