Topics in dynamic programming

Dynamic programming is an essential tool lying at the heart of many problems in the modern theory of economic dynamics. Due to its versatility in solving dynamic optimization problems, it can be used to study the decisions of households, firms, governments, and other economic agents with a wide range of applications in macroeconomics and finance. Dynamic programming transforms dynamic optimization problems to a class of functional equations, the Bellman equations, which can be solved via appropriate mathematical tools. One of the most important tools is the contraction mapping theorem, a fixed point theorem that can be used to solve the Bellman equation under the usual discounting assumption for economic agents. However, many recent economic models often make alternative discounting assumptions under which contraction no longer holds. This is the primary motivation for the thesis. This thesis is a re-examination of the standard discrete-time infinite horizon dynamic programming theory under two different discounting specifications: state-dependent discounting and negative discounting. For the case of state-dependent discounting, the standard discounting condition is generalized to an "eventual discounting" condition, under which the Bellman operator is a contraction in the long run, instead of a contraction in one step. For negative discounting, the theory of monotone concave operators is used to derive a unique solution to the Bellman equation; no contraction mapping arguments are required. The core results of the standard theory are extended to these two cases and economic applications are discussed

HEDNet: A Hierarchical Encoder-Decoder Network for 3D Object Detection in Point Clouds

3D object detection in point clouds is important for autonomous driving systems. A primary challenge in 3D object detection stems from the sparse distribution of points within the 3D scene. Existing high-performance methods typically employ 3D sparse convolutional neural networks with small kernels to extract features. To reduce computational costs, these methods resort to submanifold sparse convolutions, which prevent the information exchange among spatially disconnected features. Some recent approaches have attempted to address this problem by introducing large-kernel convolutions or self-attention mechanisms, but they either achieve limited accuracy improvements or incur excessive computational costs. We propose HEDNet, a hierarchical encoder-decoder network for 3D object detection, which leverages encoder-decoder blocks to capture long-range dependencies among features in the spatial space, particularly for large and distant objects. We conducted extensive experiments on the Waymo Open and nuScenes datasets. HEDNet achieved superior detection accuracy on both datasets than previous state-of-the-art methods with competitive efficiency. The code is available at https://github.com/zhanggang001/HEDNet.Comment: Accepted by NeurIPS 202

PoseFusion: Robust Object-in-Hand Pose Estimation with SelectLSTM

Accurate estimation of the relative pose between an object and a robot hand is critical for many manipulation tasks. However, most of the existing object-in-hand pose datasets use two-finger grippers and also assume that the object remains fixed in the hand without any relative movements, which is not representative of real-world scenarios. To address this issue, a 6D object-in-hand pose dataset is proposed using a teleoperation method with an anthropomorphic Shadow Dexterous hand. Our dataset comprises RGB-D images, proprioception and tactile data, covering diverse grasping poses, finger contact states, and object occlusions. To overcome the significant hand occlusion and limited tactile sensor contact in real-world scenarios, we propose PoseFusion, a hybrid multi-modal fusion approach that integrates the information from visual and tactile perception channels. PoseFusion generates three candidate object poses from three estimators (tactile only, visual only, and visuo-tactile fusion), which are then filtered by a SelectLSTM network to select the optimal pose, avoiding inferior fusion poses resulting from modality collapse. Extensive experiments demonstrate the robustness and advantages of our framework. All data and codes are available on the project website: https://elevenjiang1.github.io/ObjectInHand-Dataset

Coal Ignition Temperature in Oxygen-Enriched CFB Boiler

The oxygen-enriched Circulating fluidized bed (CFB) combustion technology is a new method to reduce CO2 emissions. The coal ignition temperature, Ti F, in an oxygen-enriched CFB boiler is an important parameter for designing the startup burner and for choosing the operating strategy during the startup process. The combustion of five types of coal under four different atmospheres (air, O2 27 %, O2 40%, O2 53%, CO2 as balance gas) was measured in a laboratory scale fluidized bed (FB) with an under-bed preheat system. Using thermocouples and a Gas Analyzer, the changes in bed temperature and the concentration of the different components, such as O2, CO2 and CO, in flue gas were directly measured to determine Ti F. It was found that Ti F decreased with increasing O2 concentration. The differences between the ignition temperatures determined in air and with 27 % O2 were not significant. At lower bed temperatures, for two coal types with higher volatiles, a two stage-ignition for volatiles and char was observed under a high O2 concentration. The time delay between the two stages decreased and finally merged into one with increasing bed temperature. Similar results were obtained in air. The coal with the higher volatile content had a lower ignition temperature in an oxygen-enriched CFB. Comparison of the ignition temperatures obtained by different methods and the feed temperatures in industrial CFB boilers showd that the measured result in a fluidized bed can be used as a reference for oxygen-enriched CFB boilers

Co-movement Pattern Mining from Videos

Co-movement pattern mining from GPS trajectories has been an intriguing subject in spatial-temporal data mining. In this paper, we extend this research line by migrating the data source from GPS sensors to surveillance cameras, and presenting the first investigation into co-movement pattern mining from videos. We formulate the new problem, re-define the spatial-temporal proximity constraints from cameras deployed in a road network, and theoretically prove its hardness. Due to the lack of readily applicable solutions, we adapt existing techniques and propose two competitive baselines using Apriori-based enumerator and CMC algorithm, respectively. As the principal technical contributions, we introduce a novel index called temporal-cluster suffix tree (TCS-tree), which performs two-level temporal clustering within each camera and constructs a suffix tree from the resulting clusters. Moreover, we present a sequence-ahead pruning framework based on TCS-tree, which allows for the simultaneous leverage of all pattern constraints to filter candidate paths. Finally, to reduce verification cost on the candidate paths, we propose a sliding-window based co-movement pattern enumeration strategy and a hashing-based dominance eliminator, both of which are effective in avoiding redundant operations. We conduct extensive experiments for scalability and effectiveness analysis. Our results validate the efficiency of the proposed index and mining algorithm, which runs remarkably faster than the two baseline methods. Additionally, we construct a video database with 1169 cameras and perform an end-to-end pipeline analysis to study the performance gap between GPS-driven and video-driven methods. Our results demonstrate that the derived patterns from the video-driven approach are similar to those derived from groundtruth trajectories, providing evidence of its effectiveness