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1,066篇论文匹配“Reinforcement Learning and Planning”
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Reinforcement Learning · Planning

Pengcheng Wang, Chenran Li, Catherine Weaver, Kenta Kawamoto, Masayoshi Tomizuka, Chen Tang, Wei Zhan

Policies developed through Reinforcement Learning (RL) and Imitation Learning (IL) have shown great potential in continuous control tasks, but real-world applications often require adapting trained policies to unforeseen requirements. While fine-tuning can address such needs, it typically requires additional data and access to the original training metrics and parameters.In contrast, an online planning algorithm, if capable of meeting the additional requirements, can eliminate the necessity for extensive training phases and customize the policy without knowledge of the original training scheme or task. In this work, we propose a generic online planning algorithm for customizing continuous-control policies at the execution time, which we call Residual-MPPI. It can customize a given prior policy on new performance metrics in few-shot and even zero-shot online settings, given access to the prior action distribution alone. Through our experiments, we demonstrate that the proposed Residual-MPPI algorithm can accomplish the few-shot/zero-shot online policy customization task effectively, including customizing the champion-level racing agent, Gran Turismo Sophy (GT Sophy) 1.0, in the challenging car racing scenario, Gran Turismo Sport (GTS) environment. Code for MuJoCo experiments is included in the supplementary and will be open-sourced upon acceptance. Demo videos are available on our website: https://sites.google.com/view/residual-mppi.

Reinforcement Learning · Deep RL

Haoxin Lin, Yu-Yan Xu, Yihao Sun, Zhilong Zhang, Yi-Chen Li, Chengxing Jia, Junyin Ye, Jiaji Zhang, Yang Yu

Model-based methods in reinforcement learning offer a promising approach to enhance data efficiency by facilitating policy exploration within a dynamics model. However, accurately predicting sequential steps in the dynamics model remains a challenge due to the bootstrapping prediction, which attributes the next state to the prediction of the current state. This leads to accumulated errors during model roll-out. In this paper, we propose the Any-step Dynamics Model (ADM) to mitigate the compounding error by reducing bootstrapping prediction to direct prediction. ADM allows for the use of variable-length plans as inputs for predicting future states without frequent bootstrapping. We design two algorithms, ADMPO-ON and ADMPO-OFF, which apply ADM in online and offline model-based frameworks, respectively. In the online setting, ADMPO-ON demonstrates improved sample efficiency compared to previous state-of-the-art methods. In the offline setting, ADMPO-OFF not only demonstrates superior performance compared to recent state-of-the-art offline approaches but also offers better quantification of model uncertainty using only a single ADM.

Reinforcement Learning · Batch/Offline

Carolin Schmidt, Daniele Gammelli, James Harrison, Marco Pavone, Filipe Rodrigues

Hierarchical policies enable strong performance in many sequential decision-making problems, such as those with high-dimensional action spaces, those requiring long-horizon planning, and settings with sparse rewards. However, learning hierarchical policies from static offline datasets presents a significant challenge.Crucially, actions taken by higher-level policies may not be directly observable within hierarchical controllers, and the offline dataset might have been generated using a different policy structure, hindering the use of standard offline learning algorithms.In this work, we propose $\textit{OHIO}$: a framework for offline reinforcement learning (RL) of hierarchical policies. Our framework leverages knowledge of the policy structure to solve the $\textit{inverse problem}$, recovering the unobservable high-level actions that likely generated the observed data under our hierarchical policy.This approach constructs a dataset suitable for off-the-shelf offline training.We demonstrate our framework on robotic and network optimization problems and show that it substantially outperforms end-to-end RL methods and improves robustness. We investigate a variety of instantiations of our framework, both in direct deployment of policies trained offline and when online fine-tuning is performed. Code and data are available at https://ohio-offline-hierarchical-rl.github.io.

Reinforcement Learning · Batch/Offline

Ahana Deb, Roberto Cipollone, Anders Jonsson, Alessandro Ronca, Mohammad Sadegh Talebi

This work studies offline Reinforcement Learning (RL) in a class of non-Markovian environments called Regular Decision Processes (RDPs). In RDPs, the unknown dependency of future observations and rewards from the past interactions can be captured by some hidden finite-state automaton. For this reason, many RDP algorithms first reconstruct this unknown dependency using automata learning techniques. In this paper, we consider episodic RDPs and show that it is possible to overcome the limitations of existing offline RL algorithms for RDPs viathe introduction of two original techniques: a novel metric grounded in formal language theory and an approach based on Count-Min-Sketch (CMS). Owing to the novel language metric, our algorithm is proven to be more sample efficient than existing results, and in some problem instances admitting low complexity languages, the gain is showcased to be exponential in the episode length. The CMS-based approach removes the need for naïve counting and alleviates the memory requirements for long planning horizons. We derive Probably Approximately Correct (PAC) sample complexity bounds associated to each of these techniques, and validate the approach experimentally.

Theory · Reinforcement Learning and Planning

Xiaochi Qian, Shangtong Zhang

Off-policy learning enables a reinforcement learning (RL) agent to reason counterfactually about policies that are not executed and is one of the most important ideas in RL. It, however, can lead to instability when combined with function approximation and bootstrapping, two arguably indispensable ingredients for large-scale reinforcement learning. This is the notorious deadly triad. The seminal work Sutton et al. (2008) pioneers Gradient Temporal Difference learning (GTD) as the first solution to the deadly triad, which has enjoyed massive success thereafter. During the derivation of GTD, some intermediate algorithm, called $A^\top$TD, was invented but soon deemed inferior. In this paper, we revisit this $A^\top$TD and prove that a variant of $A^\top$TD, called $A_t^\top$TD, is also an effective solution to the deadly triad. Furthermore, this $A_t^\top$TD only needs one set of parameters and one learning rate. By contrast, GTD has two sets of parameters and two learning rates, making it hard to tune in practice. We provide asymptotic analysis for $A^\top_t$TD and finite sample analysis for a variant of $A^\top_t$TD that additionally involves a projection operator. The convergence rate of this variant is on par with the canonical on-policy temporal difference learning.

Jingbo Sun, Songjun Tu, Qichao Zhang, Haoran Li, Xin Liu, Yaran Chen, Ke Chen, Dongbin Zhao

Online unsupervised reinforcement learning (URL) can discover diverse skills via reward-free pre-training and exhibits impressive downstream task adaptation abilities through further fine-tuning.However, online URL methods face challenges in achieving zero-shot generalization, i.e., directly applying pre-trained policies to downstream tasks without additional planning or learning.In this paper, we propose a novel Dual-Value Forward-Backward representation (DVFB) framework with a contrastive entropy intrinsic reward to achieve both zero-shot generalization and fine-tuning adaptation in online URL.On the one hand, we demonstrate that poor exploration in forward-backward representations can lead to limited data diversity in online URL, impairing successor measures, and ultimately constraining generalization ability.To address this issue, the DVFB framework learns successor measures through a skill value function while promoting data diversity through an exploration value function, thus enabling zero-shot generalization.On the other hand, and somewhat surprisingly, by employing a straightforward dual-value fine-tuning scheme combined with a reward mapping technique, the pre-trained policy further enhances its performance through fine-tuning on downstream tasks, building on its zero-shot performance.Through extensive multi-task generalization experiments, DVFB demonstrates both superior zero-shot generalization (outperforming on all 12 tasks) and fine-tuning adaptation (leading on 10 out of 12 tasks) abilities, surpassing state-of-the-art URL methods.

Theory · Reinforcement Learning and Planning

Roman Belaire, Arunesh Sinha, Pradeep Varakantham

Deep Reinforcement Learning (DRL) policies are highly susceptible to adversarial noise in observations, which poses significant risks in safety-critical scenarios. The challenge inherent to adversarial perturbations is that by altering the information observed by the agent, the state becomes only partially observable. Existing approaches address this by either enforcing consistent actions across nearby states or maximizing the worst-case value within adversarially perturbed observations. However, the former suffers from performance degradation when attacks succeed, while the latter tends to be overly conservative, leading to suboptimal performance in benign settings. We hypothesize that these limitations stem from their failing to account for partial observability directly. To this end, we introduce a novel objective called Adversarial Counterfactual Error (ACoE), defined on the beliefs about the true state and balancing value optimization with robustness. To make ACoE scalable in model-free settings, we propose the theoretically-grounded surrogate objective Cumulative-ACoE (C-ACoE). Our empirical evaluations on standard benchmarks (MuJoCo, Atari, and Highway) demonstrate that our method significantly outperforms current state-of-the-art approaches for addressing adversarial RL challenges, offering a promising direction for improving robustness in DRL under adversarial conditions. Our code is available at https://github.com/romanbelaire/acoe-robust-rl.

Deep Learning · Large Language Models

Zhaolin Gao, Wenhao Zhan, Jonathan Chang, Gokul Swamy, Kianté Brantley, Jason Lee, Wen Sun

Large Language Models (LLMs) have achieved remarkable success at tasks like summarization that involve a single turn of interaction. However, they can still struggle with multi-turn tasks like dialogue that require long-term planning. Previous works on multi-turn dialogue extend single-turn reinforcement learning from human feedback (RLHF) methods to the multi-turn setting by treating all prior dialogue turns as a long context. Such approaches suffer from covariate shift: the conversations in the training set have previous turns generated by some reference policy, which means that low training error may not necessarily correspond to good performance when the learner is actually in the conversation loop. In response, we introduce REgressing the RELative FUture (REFUEL), an efficient policy optimization approach designed to address multi-turn RLHF in LLMs. REFUEL employs a single model to estimate $Q$-values and trains on self-generated data, addressing the covariate shift issue. REFUEL frames the multi-turn RLHF problem as a sequence of regression tasks on iteratively collected datasets, enabling ease of implementation. Theoretically, we prove that REFUEL can match the performance of any policy covered by the training set. Empirically, we evaluate our algorithm by using Llama-3.1-70B-it to simulate a user in conversation with our model. REFUEL consistently outperforms state-of-the-art methods such as DPO and REBEL across various settings. Furthermore, despite having only 8 billion parameters, Llama-3-8B-it fine-tuned with REFUEL outperforms Llama-3.1-70B-it on long multi-turn dialogues. Implementation of REFUEL can be found at https://github.com/ZhaolinGao/REFUEL/, and models trained by REFUEL can be found at https://huggingface.co/Cornell-AGI.

Reinforcement Learning · Batch/Offline

Mianchu Wang, Rui Yang, Xi Chen, Hao Sun, Meng Fang, Giovanni Montana

Offline Goal-Conditioned RL (GCRL) offers a feasible paradigm for learning general-purpose policies from diverse and multi-task offline datasets. Despite notable recent progress, the predominant offline GCRL methods, mainly model-free, face constraints in handling limited data and generalizing to unseen goals. In this work, we propose Goal-conditioned Offline Planning (GOPlan), a novel model-based framework that contains two key phases: (1) pretraining a prior policy capable of capturing multi-modal action distribution within the multi-goal dataset; (2) employing the reanalysis method with planning to generate imagined trajectories for funetuning policies. Specifically, we base the prior policy on an advantage-weighted conditioned generative adversarial network, which facilitates distinct mode separation, mitigating the pitfalls of out-of-distribution (OOD) actions. For further policy optimization, the reanalysis method generates high-quality imaginary data by planning with learned models for both intra-trajectory and inter-trajectory goals. With thorough experimental evaluations, we demonstrate that GOPlan achieves state-of-the-art performance on various offline multi-goal navigation and manipulation tasks. Moreover, our results highlight the superior ability of GOPlan to handle small data budgets and generalize to OOD goals.

Reinforcement Learning · Multi-agent

Saman Kazemkhani, Aarav Pandya, Daphne Cornelisse, Brennan Shacklett, Eugene Vinitsky

Multi-agent learning algorithms have been successful at generating superhuman planning in various games but have had limited impact on the design of deployed multi-agent planners. A key bottleneck in applying these techniques to multi-agent planning is that they require billions of steps of experience. To enable the study of multi-agent planning at scale, we present GPUDrive, a GPU-accelerated, multi-agent simulator built on top of the Madrona Game Engine capable of generating over a million simulation steps per second. Observation, reward, and dynamics functions are written directly in C++, allowing users to define complex, heterogeneous agent behaviors that are lowered to high-performance CUDA. Despite these low-level optimizations, GPUDrive is fully accessible through Python, offering a seamless and efficient workflow for multi-agent, closed-loop simulation. Using GPUDrive, we train reinforcement learning agents on the Waymo Open Motion Dataset, achieving efficient goal-reaching in minutes and scaling to thousands of scenarios in hours. We open-source the code and pre-trained agents at \url{www.github.com/Emerge-Lab/gpudrive}.

Reinforcement Learning · Planning

Devdhar Patel, Hava Siegelmann

Reinforcement learning (RL) is rapidly reaching and surpassing human-level control capabilities. However, state-of-the-art RL algorithms often require timesteps and reaction times significantly faster than human capabilities, which is impractical in real-world settings and typically necessitates specialized hardware. We introduce Sequence Reinforcement Learning (SRL), an RL algorithm designed to produce a sequence of actions for a given input state, enabling effective control at lower decision frequencies. SRL addresses the challenges of learning action sequences by employing both a model and an actor-critic architecture operating at different temporal scales. We propose a "temporal recall" mechanism, where the critic uses the model to estimate intermediate states between primitive actions, providing a learning signal for each individual action within the sequence. Once training is complete, the actor can generate action sequences independently of the model, achieving model-free control at a slower frequency. We evaluate SRL on a suite of continuous control tasks, demonstrating that it achieves performance comparable to state-of-the-art algorithms while significantly reducing actor sample complexity. To better assess performance across varying decision frequencies, we introduce the Frequency-Averaged Score (FAS) metric. Our results show that SRL significantly outperforms traditional RL algorithms in terms of FAS, making it particularly suitable for applications requiring variable decision frequencies. Furthermore, we compare SRL with model-based online planning, showing that SRL achieves comparable FAS while leveraging the same model during training that online planners use for planning.

Theory · Reinforcement Learning and Planning

Harin Lee, Min-hwan Oh

In our quest for a reinforcement learning (RL) algorithm that is both practical and provably optimal, we introduce EQO (Exploration via Quasi-Optimism). Unlike existing minimax optimal approaches, EQO avoids reliance on empirical variances and employs a simple bonus term proportional to the inverse of the state-action visit count. Central to EQO is the concept of *quasi-optimism*, where estimated values need not be fully optimistic, allowing for a simpler yet effective exploration strategy. The algorithm achieves the sharpest known regret bound for tabular RL under the mildest assumptions, proving that fast convergence can be attained with a practical and computationally efficient approach. Empirical evaluations demonstrate that EQO consistently outperforms existing algorithms in both regret performance and computational efficiency, providing the best of both theoretical soundness and practical effectiveness.

Reinforcement Learning · Deep RL

Yixiang Shan, Zhengbang Zhu, Ting Long, Qifan Liang, Yi Chang, Weinan Zhang, Liang Yin

The performance of offline reinforcement learning (RL) is sensitive to the proportion of high-return trajectories in the offline dataset. However, in many simulation environments and real-world scenarios, there are large ratios of low-return trajectories rather than high-return trajectories, which makes learning an efficient policy challenging. In this paper, we propose a method called Contrastive Diffuser (ContraDiff) to make full use of low-return trajectories and improve the performance of offline RL algorithms. Specifically, ContraDiff groups the states of trajectories in the offline dataset into high-return states and low-return states and treats them as positive and negative samples correspondingly. Then, it designs a contrastive mechanism to pull the planned trajectory of an agent toward high-return states and push them away from low-return states. Through the contrast mechanism, trajectories with low returns can serve as negative examples for policy learning, guiding the agent to avoid areas associated with low returns and achieve better performance. Through the contrast mechanism, trajectories with low returns provide a ``counteracting force'' guides the agent to avoid areas associated with low returns and achieve better performance.Experiments on 27 sub-optimal datasets demonstrate the effectiveness of our proposed method. Our code is publicly available at https://github.com/Looomo/contradiff.

Reinforcement Learning · Planning

Swarnadeep Saha, Archiki Prasad, Justin Chen, Peter Hase, Elias Stengel-Eskin, Mohit Bansal

Language models can be used to solve long-horizon planning problems in two distinct modes. In a fast 'System-1' mode, models directly generate plans without any explicit search or backtracking, and in a slow 'System-2' mode, they plan step-by-step by explicitly searching over possible actions. System-2 planning, while typically more effective, is also computationally more expensive and often infeasible for long plans or large action spaces. Moreover, isolated System-1 or System-2 planning ignores the user's end goals and constraints (e.g., token budget), failing to provide ways for the user to control the model's behavior. To this end, we propose the System-1.x Planner, a framework for controllable planning with language models that is capable of generating hybrid plans and balancing between the two planning modes based on the difficulty of the problem at hand. System-1.x consists of (i) a controller, (ii) a System-1 Planner, and (iii) a System-2 Planner. Based on a user-specified hybridization factor x governing the degree to which the system uses System-1 vs. System-2, the controller decomposes a planning problem into subgoals, and classifies them as easy or hard to be solved by either System-1 or System-2, respectively. We fine-tune all three components on top of a single base LLM, requiring only search traces as supervision. Experiments with two diverse planning tasks -- Maze Navigation and Blocksworld -- show that our System-1.x Planner outperforms a System-1 Planner, a System-2 Planner trained to approximate A* search, and also a symbolic planner (A* search), given a state exploration budget. We also demonstrate the following key properties of our planner: (1) controllability: by adjusting the hybridization factor x (e.g., System-1.75 vs. System-1.5) we can perform more (or less) search, improving performance, (2) flexibility: by building a neuro-symbolic variant composed of a neural System-1 planner and a symbolic System-2 planner, we can take advantage of existing symbolic methods, and (3) generalizability: by learning from different search algorithms (BFS, DFS, A*), we show that our method is robust to the choice of search algorithm used for training.

Theory · Reinforcement Learning and Planning

Wesley Suttle, Aamodh Suresh, Carlos Nieto-Granda

Entropy-based objectives are widely used to perform state space exploration in reinforcement learning (RL) and dataset generation for offline RL. Behavioral entropy (BE), a rigorous generalization of classical entropies that incorporates cognitive and perceptual biases of agents, was recently proposed for discrete settings and shown to be a promising metric for robotic exploration problems. In this work, we propose using BE as a principled exploration objective for systematically generating datasets that provide diverse state space coverage in complex, continuous, potentially high-dimensional domains. To achieve this, we extend the notion of BE to continuous settings, derive tractable $k$-nearest neighbor estimators, provide theoretical guarantees for these estimators, and develop practical reward functions that can be used with standard RL methods to learn BE-maximizing policies. Using standard MuJoCo environments, we experimentally compare the performance of offline RL algorithms for a variety of downstream tasks on datasets generated using BE, R\'{e}nyi, and Shannon entropy-maximizing policies, as well as the SMM and RND algorithms. We find that offline RL algorithms trained on datasets collected using BE outperform those trained on datasets collected using Shannon entropy, SMM, and RND on all tasks considered, and on 80\% of the tasks compared to datasets collected using Renyi entropy.

Theory · Reinforcement Learning and Planning

Jongmin Lee, Ernest Ryu

While there is an extensive body of research on the analysis of Value Iteration (VI) for discounted cumulative-reward MDPs, prior work on analyzing VI for (undiscounted) average-reward MDPs has been limited, and most prior results focus on asymptotic rates in terms of Bellman error. In this work, we conduct refined non-asymptotic analyses of average-reward MDPs, obtaining a collection of convergence results advancing our understanding of the setup. Among our new results, most notable are the $\mathcal{O}(1/k)$-rates of Anchored Value Iteration on the Bellman error under the multichain setup and the span-based complexity lower bound that matches the $\mathcal{O}(1/k)$ upper bound up to a constant factor of $8$ in the weakly communicating and unichain setups.

Deep Learning · Large Language Models

Jonathan Light, Min Cai, Weiqin Chen, Guanzhi Wang, Xiusi Chen, Wei Cheng, Yisong Yue, Ziniu Hu

Traditional reinforcement learning and planning require a lot of data and training to develop effective strategies. On the other hand, large language models (LLMs) can generalize well and perform tasks without prior training but struggle with complex planning and decision-making. We introduce **STRATEGIST**, a new approach that combines the strengths of both methods. It uses LLMs to generate and update high-level strategies in text form, while a Monte Carlo Tree Search (MCTS) algorithm refines and executes them. STRATEGIST is a general framework that optimizes strategies through self-play simulations without requiring any training data. We test STRATEGIST in competitive, multi-turn games with partial information, such as **Game of Pure Strategy (GOPS)** and **The Resistance: Avalon**, a multi-agent hidden-identity discussion game. Our results show that STRATEGIST-based agents outperform traditional reinforcement learning models, other LLM-based methods, and existing LLM agents while achieving performance levels comparable to human players.

Reinforcement Learning · Everything Else

Thomas Bush, Stephen Chung, Usman Anwar, Adrià Garriga-Alonso, David Krueger

We present the first mechanistic evidence that model-free reinforcement learning agents can learn to plan. This is achieved by applying a methodology based on concept-based interpretability to a model-free agent in Sokoban -- a commonly used benchmark for studying planning. Specifically, we demonstrate that DRC, a generic model-free agent introduced by [Guez et al. (2019)](https://arxiv.org/abs/1901.03559), uses learned concept representations to internally formulate plans that both predict the long-term effects of actions on the environment and influence action selection. Our methodology involves: (1) probing for planning-relevant concepts, (2) investigating plan formation within the agent's representations, and (3) verifying that discovered plans (in the agent's representations) have a causal effect on the agent's behavior through interventions. We also show that the emergence of these plans coincides with the emergence of a planning-like property: the ability to benefit from additional test-time compute. Finally, we perform a qualitative analysis of the planning algorithm learned by the agent and discover a strong resemblance to parallelized bidirectional search. Our findings advance understanding of the internal mechanisms underlying planning behavior in agents, which is important given the recent trend of emergent planning and reasoning capabilities in LLMs through RL.

Deep Learning · Large Language Models

Davide Paglieri, Bartłomiej Cupiał, Samuel Coward, Ulyana Piterbarg, Maciej Wołczyk, Akbir Khan, Eduardo Pignatelli, Łukasz Kuciński, Lerrel Pinto, Rob Fergus 等

Large Language Models (LLMs) and Vision Language Models (VLMs) possess extensive knowledge and exhibit promising reasoning abilities, however, they still struggle to perform well in complex, dynamic environments. Real-world tasks require handling intricate interactions, advanced spatial reasoning, long-term planning, and continuous exploration of new strategies—areas in which we lack effective methodologies for comprehensively evaluating these capabilities. To address this gap, we introduce BALROG, a novel benchmark designed to assess the agentic capabilities of LLMs and VLMs through a diverse set of challenging games. Our benchmark incorporates a range of existing reinforcement learning environments with varying levels of difficulty, including tasks that are solvable by non-expert humans in seconds to extremely challenging ones that may take years to master (e.g., the NetHack Learning Environment). We devise fine-grained metrics to measure performance and conduct an extensive evaluation of several popular open-source and closed-source LLMs and VLMs. Our findings indicate that while current models achieve partial success in the easier games, they struggle significantly with more challenging tasks. Notably, we observe severe deficiencies in vision-based decision-making, as several models perform worse when visual representations of the environments are provided. We release BALROG as an open and user-friendly benchmark to facilitate future research and development in the agentic community. Code and Leaderboard at balrogai.com

Reinforcement Learning · Multi-agent

Qixin ZHANG, Zongqi Wan, Yu Yang, Li Shen, Dacheng Tao

Coordinating multiple agents to collaboratively maximize submodular functions in unpredictable environments is a critical task with numerous applications in machine learning, robot planning and control. The existing approaches, such as the OSG algorithm, are often hindered by their poor approximation guarantees and the rigid requirement for a fully connected communication graph. To address these challenges, we firstly present a $\textbf{MA-OSMA}$ algorithm, which employs the multi-linear extension to transfer the discrete submodular maximization problem into a continuous optimization, thereby allowing us to reduce the strict dependence on a complete graph through consensus techniques. Moreover, $\textbf{MA-OSMA}$ leverages a novel surrogate gradient to avoid sub-optimal stationary points. To eliminate the computationally intensive projection operations in $\textbf{MA-OSMA}$, we also introduce a projection-free $\textbf{MA-OSEA}$ algorithm, which effectively utilizes the KL divergence by mixing a uniform distribution. Theoretically, we confirm that both algorithms achieve a regret bound of $\widetilde{O}(\sqrt{\frac{C_{T}T}{1-\beta}})$ against a  $(\frac{1-e^{-c}}{c})$-approximation to the best comparator in hindsight, where $C_{T}$ is the deviation of maximizer sequence, $\beta$ is the spectral gap of the network and $c$ is the joint curvature of submodular objectives. This result significantly improves the $(\frac{1}{1+c})$-approximation provided by the state-of-the-art OSG algorithm. Finally, we demonstrate the effectiveness of our proposed algorithms through simulation-based multi-target tracking.