ICML 2024 Papers

Physics-informed machine learning (PIML) has established itself as a new scientific paradigm which enables the seamless integration of observational data with partial differential equation (PDE) based physics models. A powerful tool for the analysis, reduction and solution of PDEs is the Lie symmetry method. Nevertheless, only recently has the integration of such symmetries into PIML frameworks begun to be explored. The present work adds to this growing literature by introducing an approach for incorporating a Lie symmetry into a physics-informed Gaussian process (GP) model. The symmetry is introduced as a constraint on the GP; either in a soft manner via virtual observations of an induced PDE called the invariant surface condition, or explicitly through the design of the kernel. Experimental results demonstrate that the use of symmetry constraints improves the performance of the GP for both forward and inverse problems, and that our approach offers competitive performance with neural networks in the low-data environment.

Bandits with feedback graphs are powerful online learning models that interpolate between the full information and classic bandit problems, capturing many real-life applications. A recent work by [Zhang et al., 2023] studies the contextual version of this problem and proposes an efficient and optimal algorithm via a reduction to online regression. However, their algorithm crucially relies on seeing the feedback graph before making each decision, while in many applications, the feedback graph is *uninformed*, meaning that it is either only revealed after the learner makes her decision or even never fully revealed at all. This work develops the first contextual algorithms for such uninformed settings, via an efficient reduction to online regression over both the losses and the graphs. Importantly, we show that it is critical to learn the graphs using *log loss* instead of squared loss to obtain favorable regret guarantees. We also demonstrate the empirical effectiveness of our algorithm on a bidding application using both synthetic and real-world data.

In classic Reinforcement Learning (RL), the agent maximizes an additive objective of the visited states, e.g., a value function. Unfortunately, objectives of this type cannot model many real-world applications such as experiment design, exploration, imitation learning, and risk-averse RL to name a few. This is due to the fact that additive objectives disregard interactions between states that are crucial for certain tasks. To tackle this problem, we introduce *Global* RL (GRL), where rewards are *globally* defined over trajectories instead of *locally* over states. Global rewards can capture *negative interactions* among states, e.g., in exploration, via submodularity, *positive interactions*, e.g., synergetic effects, via supermodularity, while mixed interactions via combinations of them. By exploiting ideas from submodular optimization, we propose a novel algorithmic scheme that converts any GRL problem to a sequence of classic RL problems and solves it efficiently with curvature-dependent approximation guarantees. We also provide hardness of approximation results and empirically demonstrate the effectiveness of our method on several GRL instances.