Model-based offline Reinforcement Learning (RL) allows agents to fully utilise pre-collected datasets without requiring additional or unethical explorations. However, applying model-based offline RL to online systems presents challenges, primarily due to the highly suboptimal (noise-filled) and diverse nature of datasets generated by online systems. To tackle these issues, we introduce the Causal Prompting Reinforcement Learning (CPRL) framework, designed for highly suboptimal and resource-constrained online scenarios. The initial phase of CPRL involves the introduction of the Hidden-Parameter Block Causal Prompting Dynamic (Hip-BCPD) to model environmental dynamics. This approach utilises invariant causal prompts and aligns hidden parameters to generalise to new and diverse online users. In the subsequent phase, a single policy is trained to address multiple tasks through the amalgamation of reusable skills, circumventing the need for training from scratch. Experiments conducted across datasets with varying levels of noise, including simulation-based and real-world offline datasets from the Dnurse APP, demonstrate that our proposed method can make robust decisions in out-of-distribution and noisy environments, outperforming contemporary algorithms. Additionally, we separately verify the contributions of Hip-BCPDs and the skill-reuse strategy to the robustness of performance. We further analyse the visualised structure of Hip-BCPD and the interpretability of sub-skills. We released our source code and the first ever real-world medical dataset for precise medical decision-making tasks.

While compressive sensing (CS) has been one of the most vibrant research fields in the past few years, most development only applies to linear models. This limits its application in many areas where CS could make a difference. This paper presents a novel extension of CS to the phase retrieval problem, where intensity measurements of a linear system are used to recover a complex sparse signal. We propose a novel solution using a lifting technique - CPRL, which relaxes the NP-hard problem to a nonsmooth semidefinite program. Our analysis shows that CPRL inherits many desirable properties from CS, such as guarantees for exact recovery. We further provide scalable numerical solvers to accelerate its implementation.

While compressive sensing (CS) has been one of the most vibrant and active research fields in the past few years, most development only applies to linear models. This limits its application and excludes many areas where CS ideas could make a difference. This paper presents a novel extension of CS to the phase retrieval problem, where intensity measurements of a linear system are used to recover a complex sparse signal. We propose a novel solution using a lifting technique -- CPRL, which relaxes the NP-hard problem to a nonsmooth semidefinite program. Our analysis shows that CPRL inherits many desirable properties from CS, such as guarantees for exact recovery.

While compressive sensing (CS) has been one of the most vibrant and active research fields in the past few years, most development only applies to linear models. This limits its application and excludes many areas where CS ideas could make a difference. This paper presents a novel extension of CS to the phase retrieval problem, where intensity measurements of a linear system are used to recover a complex sparse signal. We propose a novel solution using a lifting technique -- CPRL, which relaxes the NP-hard problem to a nonsmooth semidefinite program. Our analysis shows that CPRL inherits many desirable properties from CS, such as guarantees for exact recovery.

While compressive sensing (CS) has been one of the most vibrant and active research fields in the past few years, most development only applies to linear models. This limits its application and excludes many areas where CS ideas could make a difference. This paper presents a novel extension of CS to the phase retrieval problem, where intensity measurements of a linear system are used to recover a complex sparse signal. We propose a novel solution using a lifting technique -- CPRL, which relaxes the NP-hard problem to a nonsmooth semidefinite program. Our analysis shows that CPRL inherits many desirable properties from CS, such as guarantees for exact recovery. We further provide scalable numerical solvers to accelerate its implementation. The source code of our algorithms will be provided to the public.