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This paper studies continuous-time reinforcement learning for controlled jump-diffusion models by featuring the q-function (the continuous-time counterpart of Q-function) and the q-learning algorithms under the Tsallis entropy regularization. Contrary to the conventional Shannon entropy, the general form of Tsallis entropy renders the optimal policy not necessary a Gibbs measure, where some Lagrange multiplier and KKT multiplier naturally arise from certain constraints to ensure the learnt policy to be a probability distribution. As a consequence,the relationship between the optimal policy and the q-function also involves the Lagrange multiplier. In response, we establish the martingale characterization of the q-function under Tsallis entropy and devise two q-learning algorithms depending on whether the Lagrange multiplier can be derived explicitly or not. In the latter case, we need to consider different parameterizations of the q-function and the policy and update them alternatively. Finally, we examine two financial applications, namely an optimal portfolio liquidation problem and a non-LQ control problem. It is interesting to see therein that the optimal policies under the Tsallis entropy regularization can be characterized explicitly, which are distributions concentrate on some compact support. The satisfactory performance of our q-learning algorithm is illustrated in both examples.

LLMs have demonstrated commendable performance across diverse domains. Nevertheless, formulating high-quality prompts to instruct LLMs proficiently poses a challenge for non-AI experts. Existing research in prompt engineering suggests somewhat scattered optimization principles and designs empirically dependent prompt optimizers. Unfortunately, these endeavors lack a structured design template, incurring high learning costs and resulting in low reusability. In addition, it is not conducive to the iterative updating of prompts. Inspired by structured reusable programming languages, we propose LangGPT, a dual-layer prompt design framework as the programming language for LLMs. LangGPT has an easy-to-learn normative structure and provides an extended structure for migration and reuse. Experiments illustrate that LangGPT significantly enhances the performance of LLMs. Moreover, the case study shows that LangGPT leads LLMs to generate higher-quality responses. Furthermore, we analyzed the ease of use and reusability of LangGPT through a user survey in our online community.

This paper studies an infinite horizon optimal tracking portfolio problem using capital injection in incomplete market models. We consider the benchmark process modelled by a geometric Brownian motion with zero drift driven by some unhedgeable risk. The relaxed tracking formulation is adopted where the portfolio value compensated by the injected capital needs to outperform the benchmark process at any time, and the goal is to minimize the cost of the discounted total capital injection. In the first part, we solve the stochastic control problem when the market model is known, for which the equivalent auxiliary control problem with reflections and the associated HJB equation with a Neumann boundary condition are studied. In the second part, the market model is assumed to be unknown, for which we consider the exploratory formulation of the control problem with entropy regularizer and develop the continuous-time q-learning algorithm for the stochastic control problem with state reflections. In an illustrative example, we show the satisfactory performance of the q-learning algorithm., Comment: Optimal tracking portfolio, capital injection, incomplete market, stochastic control with reflection, continuous-time reinforcement learning, q-learning

The success of pre-training approaches on a variety of downstream tasks has revitalized the field of computer vision. Image aesthetics assessment (IAA) is one of the ideal application scenarios for such methods due to subjective and expensive labeling procedure. In this work, an unified and flexible two-phase \textbf{C}LIP-based \textbf{S}emi-supervised \textbf{K}nowledge \textbf{D}istillation paradigm is proposed, namely \textbf{\textit{CSKD}}. Specifically, we first integrate and leverage a multi-source unlabeled dataset to align rich features between a given visual encoder and an off-the-shelf CLIP image encoder via feature alignment loss. Notably, the given visual encoder is not limited by size or structure and, once well-trained, it can seamlessly serve as a better visual aesthetic learner for both student and teacher. In the second phase, the unlabeled data is also utilized in semi-supervised IAA learning to further boost student model performance when applied in latency-sensitive production scenarios. By analyzing the attention distance and entropy before and after feature alignment, we notice an alleviation of feature collapse issue, which in turn showcase the necessity of feature alignment instead of training directly based on CLIP image encoder. Extensive experiments indicate the superiority of CSKD, which achieves state-of-the-art performance on multiple widely used IAA benchmarks.

This paper studies the existence and uniqueness of a classical solution to a type of Robin boundary problems on the nonnegative orthant. We propose a new decomposition-homogenization method for the Robin boundary problem based on probabilistic representations, which leads to two auxiliary Robin boundary problems admitting some simplified probabilistic representations. The auxiliary probabilistic representations allow us to establish the existence of a unique classical solution to the original Robin boundary problem using some stochastic flow analysis., Comment: Keywords: Robin boundary problem, decomposition-homogenization method, probabilistic representation, classical solution, stochastic flow analysis

This paper studies a Merton's optimal consumption problem in an extended formulation incorporating the tracking of a benchmark process described by a geometric Brownian motion. We consider a relaxed tracking formulation such that the wealth process compensated by a fictitious capital injection outperforms the benchmark at all times. The fund manager aims to maximize the expected utility of consumption deducted by the cost of the capital injection, where the latter term can also be regarded as the expected largest shortfall of the wealth with reference to the benchmark. By introducing an auxiliary state process with reflection, we formulate and tackle an equivalent stochastic control problem by means of the dual transform and probabilistic representation, where the dual PDE can be solved explicitly. On the strength of the closed-form results, we can derive and verify the optimal feedback control for the primal control problem, allowing us to discuss some new and interesting financial implications induced by the additional risk-taking from the capital injection and the goal of tracking., Comment: Keywords: Benchmark tracking, capital injection, expected largest shortfall, consumption and portfolio choice, Neumann boundary condition

Active learning selects informative samples for annotation within budget, which has proven efficient recently on object detection. However, the widely used active detection benchmarks conduct image-level evaluation, which is unrealistic in human workload estimation and biased towards crowded images. Furthermore, existing methods still perform image-level annotation, but equally scoring all targets within the same image incurs waste of budget and redundant labels. Having revealed above problems and limitations, we introduce a box-level active detection framework that controls a box-based budget per cycle, prioritizes informative targets and avoids redundancy for fair comparison and efficient application. Under the proposed box-level setting, we devise a novel pipeline, namely Complementary Pseudo Active Strategy (ComPAS). It exploits both human annotations and the model intelligence in a complementary fashion: an efficient input-end committee queries labels for informative objects only; meantime well-learned targets are identified by the model and compensated with pseudo-labels. ComPAS consistently outperforms 10 competitors under 4 settings in a unified codebase. With supervision from labeled data only, it achieves 100% supervised performance of VOC0712 with merely 19% box annotations. On the COCO dataset, it yields up to 4.3% mAP improvement over the second-best method. ComPAS also supports training with the unlabeled pool, where it surpasses 90% COCO supervised performance with 85% label reduction. Our source code is publicly available at https://github.com/lyumengyao/blad., Comment: CVPR 2023 highlight

This paper studies stochastic control problems motivated by optimal consumption with wealth benchmark tracking. The benchmark process is modeled by a combination of a geometric Brownian motion and a running maximum process, indicating its increasing trend in the long run. We consider a relaxed tracking formulation such that the wealth compensated by the injected capital always dominates the benchmark process. The stochastic control problem is to maximize the expected utility of consumption deducted by the cost of the capital injection under the dynamic floor constraint. By introducing two auxiliary state processes with reflections, an equivalent auxiliary control problem is formulated and studied, which leads to the HJB equation with two Neumann boundary conditions. We establish the existence of a unique classical solution to the dual PDE using some novel probabilistic representations involving the local time of some dual processes together with a tailor-made decomposition-homogenization technique. The proof of the verification theorem on the optimal feedback control can be carried out by some stochastic flow analysis and technical estimations of the optimal control., Comment: Keywords: Relaxed benchmark tracking, optimal consumption, Neumann boundary conditions, probabilistic representation, reflected diffusion process

Local discriminative representation is needed in many medical image analysis tasks such as identifying sub-types of lesion or segmenting detailed components of anatomical structures. However, the commonly applied supervised representation learning methods require a large amount of annotated data, and unsupervised discriminative representation learning distinguishes different images by learning a global feature, both of which are not suitable for localized medical image analysis tasks. In order to avoid the limitations of these two methods, we introduce local discrimination into unsupervised representation learning in this work. The model contains two branches: one is an embedding branch which learns an embedding function to disperse dissimilar pixels over a low-dimensional hypersphere; and the other is a clustering branch which learns a clustering function to classify similar pixels into the same cluster. These two branches are trained simultaneously in a mutually beneficial pattern, and the learnt local discriminative representations are able to well measure the similarity of local image regions. These representations can be transferred to enhance various downstream tasks. Meanwhile, they can also be applied to cluster anatomical structures from unlabeled medical images under the guidance of topological priors from simulation or other structures with similar topological characteristics. The effectiveness and usefulness of the proposed method are demonstrated by enhancing various downstream tasks and clustering anatomical structures in retinal images and chest X-ray images., Comment: Accepted by IPMI2021