February 2026

Table of Links Abstract and 1. Introduction 2. Financial Market Model and Worst-Case Optimization Problem 3. Solution to the Post-Crash Problem 4. Solution to the Pre-Crash Problem 5. A BSDE Characterization of Indifferences Strategies 6. The Markovian Case 7. Numerical Experiments Acknowledgments and References Appendix A. Proofs from Section 3 Appendix B. Proofs of BASDE Results from Section 5 Appendix C. Proofs of (CIR) Results from Section 6 Abstract. We study and solve the worst-case optimal portfolio problem […]

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Reinforcement learning (RL) agents often suffer from high sample complexity in sparse or delayed reward settings due to limited prior structure. Large language models (LLMs) can provide subgoal decompositions, plausible trajectories, and abstract priors that facilitate early learning. However, heavy reliance on LLM supervision introduces scalability constraints and dependence on potentially unreliable signals. We propose MIRA (Memory-Integrated Reinforcement Learning Agent), which incorporates a structured, evolving memory graph to guide early training. The graph stores decision-relevant information, including trajectory […]

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Lately, you can’t open YouTube, read the news, or scroll LinkedIn without getting hit by the same narrative. Every day, another CEO confidently declares that software engineers are obsolete and that anyone can prompt their way to the next billion-dollar app. And to be fair, the AI world has completely tanked the barrier to entry for prototyping. With AI integrated into workflows, a lean team of 10 people can ship faster and better than a firm with 200 […]

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Over the last ten years, running has become a huge part of my life. I’m not sure how useful this write-up will be to others, but running preoccupies me enough that I feel the need to document the journey and externalize my thoughts. On 14.02.2026 (Valentine’s day) I ran my longest trail race: Trail du Mont Agel in Monaco. I expected a picturesque and exciting, yet challenging, adventure. I prepared for it by running 20–30 km every week […]

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Reached the stage of parallel agent psychosis where I’ve lost a whole feature – I know I had it yesterday, but I can’t seem to find the branch or worktree or cloud instance or checkout with it in. … found it! Turns out I’d been hacking on a random prototype in /tmp and then my computer crashed and rebooted and I lost the code… but it’s all still there in ~/.claude/projects/ session logs and Claude Code can extract […]

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Data collection is a critical component of modern statistical and machine learning pipelines, particularly when data must be gathered from multiple heterogeneous sources to study a target population of interest. In many use cases, such as medical studies or political polling, different sources incur different sampling costs. Observations often have associated group identities (for example, health markers, demographics, or political affiliations) and the relative composition of these groups may differ substantially, both among the source populations and between […]

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State space models (SSMs) have recently emerged for modeling long-range dependency in sequence data, with much simplified computational costs than modern alternatives, such as transformers. Advancing SMMs to graph structured data, especially for large graphs, is a significant challenge because SSMs are sequence models and the shear graph volumes make it very expensive to convert graphs as sequences for effective learning. In this paper, we propose COMBA to tackle large graph learning using state space models, with two […]

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Artificial intelligence (AI) has increasingly transformed medical prognostics by enabling rapid and accurate analysis across imaging and pathology. However, the investigation of machine learning predictions applied to prospectively collected, standardized data from observational clinical intervention trials remains underexplored, despite its potential to reduce costs and improve patient outcomes. Chronic rhinosinusitis (CRS), a persistent inflammatory disease of the paranasal sinuses lasting more than three months, imposes a substantial burden on quality of life (QoL) and societal cost. Although many […]

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Stochastic gradient descent (SGD) is a cornerstone algorithm for high-dimensional optimization, renowned for its empirical successes. Recent theoretical advances have provided a deep understanding of how SGD enables feature learning in high-dimensional nonlinear models, most notably the textit{single-index model} with i.i.d. data. In this work, we study the sequential learning problem for single-index models, also known as generalized linear bandits or ridge bandits, where SGD is a simple and natural solution, yet its learning dynamics remain largely unexplored. […]

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