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We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to solve due to its inherent non-convexity. In this paper, we demonstrate that, under mild conditions, the robust risk evaluation of a given policy can be expressed in an equivalent recursive form. Furthermore, assuming stagewise independence, we derive equivalent dynamic programming reformulations to find an optimal robust policy that is time-consistent and well-defined on unseen sample paths. Our reformulations reconcile two modeling frameworks: the multistage-static formulation (with nested distance) and the multistage-dynamic formulation (with one-period Wasserstein distance). Moreover, we identify tractable cases when the value functions can be computed efficiently using convex optimization techniques., Comment: First appeared online at https://optimization-online.org/?p=20641 on Oct 15, 2022

Despite the recent successes of multi-agent reinforcement learning (MARL) algorithms, efficiently adapting to co-players in mixed-motive environments remains a significant challenge. One feasible approach is to hierarchically model co-players' behavior based on inferring their characteristics. However, these methods often encounter difficulties in efficient reasoning and utilization of inferred information. To address these issues, we propose Hierarchical Opponent modeling and Planning (HOP), a novel multi-agent decision-making algorithm that enables few-shot adaptation to unseen policies in mixed-motive environments. HOP is hierarchically composed of two modules: an opponent modeling module that infers others' goals and learns corresponding goal-conditioned policies, and a planning module that employs Monte Carlo Tree Search (MCTS) to identify the best response. Our approach improves efficiency by updating beliefs about others' goals both across and within episodes and by using information from the opponent modeling module to guide planning. Experimental results demonstrate that in mixed-motive environments, HOP exhibits superior few-shot adaptation capabilities when interacting with various unseen agents, and excels in self-play scenarios. Furthermore, the emergence of social intelligence during our experiments underscores the potential of our approach in complex multi-agent environments., Comment: Accepted at ICML 2024

Due to the permanent harm to human health and ecosystem balance, antibiotic pollution in water has become an important direction of current environmental governance. Spherical metal oxides (SMOs) have been frequently utilized as effective heterogeneous photocatalysts for the efficient degradation of antibiotics due to the unique properties (e.g., strong light absorption ability, high separation efficiency of photo-generated electron hole pairs, and good catalytic activity). This review will firstly focus on summarizing the rational design and synthesis of SMOs with various tuned microstructures such as hollow, porous shell, yolk shell, core shell, and nanoflowers. These structures can expose more active sites, achieve a higher utilization rate of light, enhance the mass transfer efficiency and improve the effective diffusion of reactive oxygen species (ROS). Secondly, this review will mainly analyze the intrinsic relationship between the structure of SMOs and its photocatalytic property, the ability to generate ROS, and the degradation pathway for antibiotics. Moreover, the photocatalytic mechanisms and recent progress of different SMOs catalysts for degrading typical antibiotics are compared in detail. Finally, challenges and prospects of future direction in the development of SMOs for antibiotic degradation are reviewed. It is expected to provide a rational design of SMOs catalysts for efficient photocatalytic degradation of environmental pollutants.

Rational design and green synthesis of low-cost and robust catalysts efficient for the selective oxidation of various alcohols are full of challenges. Herein, we report a fast and solvent-free arc-melting (AM) method to controllably synthesize semimetal CoSi alloy (abbreviated as AM-CoSi) that is efficient for the base- and solvent-free oxidation of six types of aromatic alcohols. X-ray absorption fine structure (XAFS), electron paramagnetic resonance (EPR), and aberration corrected high angle annular dark field scanning transmission electron microscope (AC HAADF-STEM) confirmed the successful synthesis of AM-CoSi with rich Si vacancy (Siv). The as-prepared CoSi alloy catalysts exhibit an order of magnitude activity enhancement in the oxidation of model reactant benzyl alcohol (BAL) to benzyl benzoate (BBE) compared with its mono counterparts, whereas 70 % yield of BBE which is the highest yield to date. Experimental results and DFT calculations well verify that the CoSi alloy structure improves the BAL conversion and Si vacancy mainly contributes to the generation of BBE. After that, CoSi alloy maintains high stability and a potential pathway is rationally proposed. Besides, CoSi alloy also efficiently works for the selective oxidation of various alcohols with different groups. This work demonstrates for the first time that semimetal CoSi alloy is robust for the green oxidation of various alcohols and provides a vast opportunity for reasonable design and application of other semimetal alloy catalysts., Comment: 22 pages, 6 figures

Iron-based molybdenum disulfide (Fe-MoS$_2$) has emerged as a Fenton-like catalyst for the highly efficient degradation of antibiotics, but the structure-activity relationship remains elusive. Herein, garland-like MIL-101(Fe)/MoS$_2$ nanosheets (MMS) with dual metal active sites (Fe and Mo) and rich sulfur vacancies were fabricated to directly activate peroxymonosulfate (PMS) for fast degradation of different organic pollutants (phenols, dyes and drugs), even in real water bodies. The MMS exhibited extremely fast catalytic rate constant of 0.289 min$^{-1}$ in the degradation of sulfamethoxazole (SMX), which was about 36 and 29 times that of single MoS$_2$ (0.008 min$^{-1}$) and MIL-101(Fe) (0.01 min$^{-1}$). Moreover, MMS with good stability and reusability could reach 92% degradation of SMX after 5 cycles. Quenching experiments and electron spin resonance (ESR) tests revealed that hydroxyl radicals (.OH) and singlet oxygen ($^1$O$_2$) were the dominant reactive oxygen species (ROS) for SMX degradation. The integration of experimental works, characterization techniques and density functional theory (DFT) calculations unraveled that the formation of sulfur vacancies in MMS catalyst could expose more Mo sites, improve the charge density and boost the electron transfer, which was conducive to accelerating the Fe$^{3+}$/Fe$^{2+}$ cycle for enhancing the activation of PMS. Finally, the C-N, N-O, S-N, C-O and C-S bonds of SMX were easily attacked by ROS to generate the nontoxic intermediates in the MMS/PMS/SMX system. This study offers a new approach to designing high-performance Fe-MoS$_2$ catalysts for the removal of organic pollutants.

With the rapid industrial development, many dye pollutants have entered the water, along with heavy metals like As, leading to complex pollution that threatens the ecological environment and human health. Therefore, designing an effective strategy for treating complex dye wastewater is urgent. Herein, we have constructed high-purity pyrite FeS$_2$ nanoplates as bifunctional catalysts for the simultaneous removal of dyes and arsenite (As(III)).

The coexistence of tetracycline (TC) and arsenite (As(III)) in livestock wastewater threatens public health, and the heterogeneous Fenton-like system is a practical approach for the simultaneous removal of TC and As(III). In this work, fine CoFe$_2$O$_4$ nanoparticles are facilely anchored on heretically porous carbon (CoFe$_2$O$_4$@PC) via a microwave-assisted calcination method and used for eliminating TC and As(III) via peroxymonosulfate (PMS) activation.

We propose a new framework to design controllers for high-dimensional nonlinear systems. The control is designed through the iterative linear quadratic regulator (ILQR), an algorithm that computes control by iteratively applying the linear quadratic regulator on the local linearization of the system at each time step. Since ILQR is computationally expensive, we propose to first construct reduced-order models (ROMs) of the high-dimensional nonlinear system. We derive nonlinear ROMs via projection, where the basis is computed via balanced truncation (BT) and LQG balanced truncation (LQG-BT). Numerical experiments are performed on a semi-discretized nonlinear Burgers equation. We find that the ILQR algorithm produces good control on ROMs constructed either by BT or LQG-BT, with BT-ROM based controllers outperforming LQG-BT slightly for very low-dimensional systems.