ICLR 2026 论文列表

International Conference on Learning Representations

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5,358篇论文

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  • Oral
    2244.2%
  • Poster
    5,13495.8%

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Refining Hybrid Genetic Search for CVRP via Reinforcement Learning-Finetuned LLM

Rongjie Zhu, Cong Zhang, Zhiguang Cao

展开摘要

While large language models (LLMs) are increasingly used as automated heuristic designers for vehicle routing problems (VRPs), current state-of-the-art methods predominantly rely on prompting massive, general-purpose models like GPT-4. This work challenges that paradigm by demonstrating that a smaller, specialized LLM, when meticulously fine-tuned, can generate components that surpass expert-crafted heuristics within advanced solvers. We propose RFTHGS, a novel Reinforcement learning (RL) framework for Fine-Tuning a compact LLM to generate high-performance crossover operators for the Hybrid Genetic Search (HGS) solver, applied to the Capacitated VRP (CVRP). Our method employs a multi-tiered, curriculum-based reward function that progressively guides the LLM to master generating first compilable, then executable, and finally, superior-performing operators that exceed human expert designs. This is coupled with an operator caching mechanism that discourages plagiarism and promotes diversity during training. Comprehensive experiments show that our fine-tuned LLM produces crossover operators which significantly outperform the expert-designed ones in HGS. The performance advantage remains consistent, generalizing from small-scale instances to large-scale problems with up to 1000 nodes. Furthermore, RFTHGS exceeds the performance of leading neuro-combinatorial baselines, prompt-based methods, and commercial LLMs such as GPT-4o and GPT-4o-mini.

Poster
EXPO: Stable Reinforcement Learning with Expressive Policies

Perry Dong, Qiyang Li, Dorsa Sadigh, Chelsea Finn

展开摘要

We study the problem of training and fine-tuning expressive policies with online reinforcement learning (RL) given an offline dataset. Training expressive policy classes with online RL present a unique challenge of stable value maximization. Unlike simpler Gaussian policies commonly used in online RL, expressive policies like diffusion and flow-matching policies are parameterized by a long denoising chain, which hinders stable gradient propagation from actions to policy parameters when optimizing against some value function. Our key insight is that we can address stable value maximization by avoiding direct optimization over value with the expressive policy and instead construct an on-the-fly RL policy to maximize Q-value. We propose Expressive Policy Optimization (EXPO), a sample-efficient online RL algorithm that utilizes an on-the-fly policy to maximize value with two parameterized policies -- a larger expressive base policy trained with a stable imitation learning objective and a light-weight Gaussian edit policy that edits the actions sampled from the base policy toward a higher value distribution. The on-the-fly policy optimizes the actions from the base policy with the learned edit policy and chooses the value maximizing action from the base and edited actions for both sampling and temporal-difference (TD) backup. Our approach yields up to 2-3x improvement in sample efficiency on average over prior methods both in the setting of fine-tuning a pretrained policy given offline data and in leveraging offline data to train online.

Poster
Automating the Refinement of Reinforcement Learning Specifications

Tanmay Ambadkar, Đorđe Žikelić, Abhinav Verma

展开摘要

Logical specifications have been shown to help reinforcement learning algorithms in achieving complex tasks. However, when a task is under-specified, agents might fail to learn useful policies. In this work, we explore the possibility of improving coarse-grained logical specifications via an exploration-guided strategy. We propose **AutoSpec**, a framework that searches for a logical specification refinement whose satisfaction implies satisfaction of the original specification, but which provides additional guidance therefore making it easier for reinforcement learning algorithms to learn useful policies. **AutoSpec** is applicable to reinforcement learning tasks specified via the SpectRL specification logic. We exploit the compositional nature of specifications written in SpectRL, and design four refinement procedures that modify the abstract graph of the specification by either refining its existing edge specifications or by introducing new edge specifications. We prove that all four procedures maintain specification soundness, i.e. any trajectory satisfying the refined specification also satisfies the original. We then show how **AutoSpec** can be integrated with existing reinforcement learning algorithms for learning policies from logical specifications. Our experiments demonstrate that **AutoSpec** yields promising improvements in terms of the complexity of control tasks that can be solved, when refined logical specifications produced by **AutoSpec** are utilized.

Poster
Q-learning with Posterior Sampling

Priyank Agrawal, Shipra Agrawal, Azmat Azati

展开摘要

Bayesian posterior sampling techniques have demonstrated superior empirical performance in many exploration-exploitation settings. However, their theoretical analysis remains a challenge, especially in complex settings like reinforcement learning. In this paper, we introduce Q-Learning with Posterior Sampling (PSQL), a simple Q-learning-based algorithm that uses Gaussian posteriors on Q-values for exploration, akin to the popular Thompson Sampling algorithm in the multi-armed bandit setting. We show that in the tabular episodic MDP setting, PSQL achieves a regret bound of $\tilde O(H^2\sqrt{SAT})$, closely matching the known lower bound of $\Omega(H\sqrt{SAT})$. Here, S, A denote the number of states and actions in the underlying Markov Decision Process (MDP), and $T=KH$ with $K$ being the number of episodes and $H$ being the planning horizon. Our work provides several new technical insights into the core challenges in combining posterior sampling with dynamic programming and TD-learning-based RL algorithms, along with novel ideas for resolving those difficulties. We hope this will form a starting point for analyzing this efficient and important algorithmic technique in even more complex RL settings.

Poster
Beyond Penalization: Diffusion-based Out-of-Distribution Detection and Selective Regularization in Offline Reinforcement Learning

Qingjun Wang, Hongtu Zhou, Hang Yu, Junqiao Zhao, Yanping Zhao, Chen Ye, Ziqiao Wang, Guang Chen

展开摘要

Offline reinforcement learning (RL) faces a critical challenge of overestimating the value of out-of-distribution (OOD) actions. Existing methods mitigate this issue by penalizing unseen samples, yet they fail to accurately identify OOD actions and may suppress beneficial exploration beyond the behavioral support. Although several methods have been proposed to differentiate OOD samples with distinct properties, they typically rely on restrictive assumptions about the data distribution and remain limited in discrimination ability. To address this problem, we propose $\textbf{DOSER}$ ($\textbf{D}$iffusion-based $\textbf{O}$OD Detection and $\textbf{SE}$lective $\textbf{R}$egularization), a novel framework that goes beyond uniform penalization. DOSER trains two diffusion models to capture the behavior policy and state distribution, using single-step denoising reconstruction error as a reliable OOD indicator. During policy optimization, it further distinguishes between beneficial and detrimental OOD actions by evaluating predicted transitions, selectively suppressing risky actions while encouraging exploration of high-potential ones. Theoretically, we prove that DOSER is a $\gamma$-contraction and therefore admits a unique fixed point with bounded value estimates. We further provide an asymptotic performance guarantee relative to the optimal policy under model approximation and OOD detection errors. Across extensive offline RL benchmarks, DOSER consistently attains superior performance to prior methods, especially on suboptimal datasets.

Poster
Learning Efficient and Interpretable Multi-Agent Communication

Wei Du, Benyu Wu, Yuqing Sun, Wei Guo, Yuntao Du, Zhongmin Yan, Guoxian Yu, Lizhen Cui

展开摘要

Effective communication is crucial for multi-agent cooperation in partially observable environments. However, a fundamental trilemma exists among task performance, communication efficiency, and human interpretability. To resolve this, we propose a multi-agent communication framework via $\textbf{G}$rounding $\textbf{L}$anguage and $\textbf{C}$ontrastive learning (GLC) to learns efficient and interpretable communication protocols. Specifically, GLC employs an autoencoder to learn discretized and compressed communication symbols, ensuring high communication efficiency. These symbols are then semantically aligned with human concepts using data generated by a Large Language Model (LLM), making them human-interpretable. Furthermore, a contrastive learning objective is introduced to ensure consistency and mutual intelligibility among all agents, thereby securing high task utility. GLC dynamically balances these objectives by the Information Bottleneck principle. Extensive experiments show that GLC outperforms state-of-the-art methods across multiple benchmarks, delivering superior task performance, higher communication efficiency, and enhanced human interpretability.

Poster
DR-SAC: Distributionally Robust Soft Actor-Critic for Reinforcement Learning under Uncertainty

Mingxuan Cui, Duo Zhou, Yuxuan Han, Grani A. Hanasusanto, Qiong Wang, Huan Zhang, Zhengyuan Zhou

展开摘要

Deep reinforcement learning (RL) has achieved remarkable success, yet its deployment in real-world scenarios is often limited by vulnerability to environmental uncertainties. Distributionally robust RL (DR-RL) algorithms have been proposed to resolve this challenge, but existing approaches are largely restricted to value-based methods in tabular settings. In this work, we introduce Distributionally Robust Soft Actor-Critic (DR-SAC), the first actor–critic based DR-RL algorithm for offline learning in continuous action spaces. DR-SAC maximizes the entropy-regularized rewards against the worst possible transition models within an KL-divergence constrained uncertainty set. We derive the distributionally robust version of the soft policy iteration with a convergence guarantee and incorporate a generative modeling approach to estimate the unknown nominal transition models. Experiment results on five continuous RL tasks demonstrate our algorithm achieves up to $9.8\times$ higher average reward than the SAC baseline under common perturbations. Additionally, DR-SAC significantly improves computing efficiency and applicability to large-scale problems compared with existing DR-RL algorithms.

Poster
Optimal Robust Subsidy Policies for Irrational Agent in Principal-Agent MDPs

Bowen Hu, Yixin Tao

展开摘要

We investigate a principal-agent problem modeled within a Markov Decision Process, where the principal and the agent have their own rewards. The principal can provide subsidies to influence the agent’s action choices, and the agent’s resulting action policy determines the rewards accrued to the principal. Our focus is on designing a robust subsidy scheme that maximizes the principal’s cumulative expected return, even when the agent displays bounded rationality and may deviate from the optimal action policy after receiving subsidies. As a baseline, we first analyze the case of a perfectly rational agent and show that the principal’s optimal subsidy coincides with the policy that maximizes social welfare, the sum of the utilities of both the principal and the agent. We then introduce a bounded-rationality model: the globally $\epsilon$-incentive-compatible agent, who accepts any policy whose expected cumulative utility lies within $\epsilon$ of the personal optimum. In this setting, we prove that the optimal robust subsidy scheme problem simplifies to a one-dimensional concave optimization. This reduction not only yields a clean analytical solution but also highlights a key structural insight: optimal subsidies are concentrated along the social-welfare-maximizing trajectories. We further characterize the loss in social welfare—the degradation under the robust subsidy scheme compared to the maximum achievable—and provide an upper bound on this loss. Finally, we investigate a finer-grained, state-wise $\epsilon$-incentive-compatible model. In this setting, we show that under two natural definitions of state-wise incentive-compatibility, the problem becomes intractable: one definition results in non-Markovian agent action policy, while the other renders the search for an optimal subsidy scheme NP-hard.

Poster
In-Context Compositional Q-Learning for Offline Reinforcement Learning

Qiushui Xu, Yu-Hao Huang, Yushu Jiang, Wenliang Zheng, Lei Song, Jinyu Wang, Jiang Bian

展开摘要

Accurately estimating the Q-function is a central challenge in offline reinforcement learning. However, existing approaches often rely on a single global Q-function, which struggles to capture the compositional nature of tasks involving diverse subtasks. We propose In-context Compositional Q-Learning ($\texttt{ICQL}$), the first offline RL framework that formulates Q-learning as a contextual inference problem, using linear Transformers to adaptively infer local Q-functions from retrieved transitions without explicit subtask labels. Theoretically, we show that under two assumptions—linear approximability of the local Q-function and accurate weight inference from retrieved context—$\texttt{ICQL}$ achieves bounded Q-function approximation error, and supports near-optimal policy extraction. Empirically, $\texttt{ICQL}$ substantially improves performance in offline settings: improving performance in Kitchen tasks by up to 29. 46\%, and in Gym and Adroit tasks by up to 6\%. These results highlight the underexplored potential of in-context learning for robust and compositional value estimation, positioning $\texttt{ICQL}$ as a principled and effective framework for offline RL.

Poster
Adaptive Rollout Allocation for Online Reinforcement Learning with Verifiable Rewards

Hieu Trung Nguyen, Bao Nguyen, Wenao Ma, Yuzhi Zhao, Ruifeng She, Viet Anh Nguyen

展开摘要

Sampling efficiency is a key bottleneck in reinforcement learning with verifiable rewards. Existing group-based policy optimization methods, such as GRPO, allocate a fixed number of rollouts for all training prompts. This uniform allocation implicitly treats all prompts as equally informative, and could lead to inefficient computational budget usage and impede training progress. We introduce VIP, a Variance-Informed Predictive allocation strategy that allocates a given rollout budget to the prompts in the incumbent batch to minimize the expected gradient variance of the policy update. At each iteration, VIP uses a lightweight Gaussian process model to predict per-prompt success probabilities based on recent rollouts. These probability predictions are translated into variance estimates, which are then fed into a convex optimization problem to determine the optimal rollout allocations under a hard compute budget constraint. Empirical results show that VIP consistently improves sampling efficiency and achieves higher performance than uniform or heuristic allocation strategies in multiple benchmarks.

Poster
ReFORM: Reflected Flows for On-support Offline RL via Noise Manipulation

Songyuan Zhang, Oswin So, H M Sabbir Ahmad, Eric Yang Yu, Matthew Cleaveland, Mitchell Black, Chuchu Fan

展开摘要

Offline reinforcement learning (RL) aims to learn the optimal policy from a fixed dataset generated by behavior policies without additional environment interactions. One common challenge that arises in this setting is the out-of-distribution (OOD) error, which occurs when the policy leaves the training distribution. Prior methods penalize a statistical distance term to keep the policy close to the behavior policy, but this constrains policy improvement and may not completely prevent OOD actions. Another challenge is that the optimal policy distribution can be multimodal and difficult to represent. Recent works apply diffusion or flow policies to address this problem, but it is unclear how to avoid OOD errors while retaining policy expressiveness. We propose ReFORM, an offline RL method based on flow policies that enforces the less restrictive support constraint by construction. ReFORM learns a behavior cloning (BC) flow policy with a bounded source distribution to capture the support of the action distribution, then optimizes a reflected flow that generates bounded noise for the BC flow while keeping the support, to maximize the performance. Across 40 challenging tasks from the OGBench benchmark with datasets of varying quality and using a constant set of hyperparameters for all tasks, ReFORM dominates all baselines with hand-tuned hyperparameters on the performance profile curves.

Poster
Potentially Optimal Joint Actions Recognition for Cooperative Multi-Agent Reinforcement Learning

Chang Huang, Shatong Zhu, Junqiao Zhao, Hongtu Zhou, Hai Zhang, Di Zhang, Chen Ye, Ziqiao Wang, Guang Chen

展开摘要

Value function factorization is widely used in cooperative multi-agent reinforcement learning (MARL). Existing approaches often impose monotonicity constraints between the joint action value and individual action values to enable decentralized execution. However, such constraints limit the expressiveness of value factorization, restricting the range of joint action values that can be represented and hindering the learning of optimal policies. To address this, we propose Potentially Optimal Joint Actions Weighting (POW), a method that ensures optimal policy recovery where existing approximate weighting strategies may fail. POW iteratively identifies potentially optimal joint actions and assigns them higher training weights through a theoretically grounded iterative weighted training process. We prove that this mechanism guarantees recovery of the true optimal policy, overcoming the limitations of prior heuristic weighting strategies. POW is architecture-agnostic and can be seamlessly integrated into existing value factorization algorithms. Extensive experiments on matrix games, difficulty-enhanced predator-prey tasks, SMAC, SMACv2, and a highway-env intersection scenario show that POW substantially improves stability and consistently surpasses state-of-the-art value-based MARL methods.

Poster
PolicyFlow: Policy Optimization with Continuous Normalizing Flow in Reinforcement Learning

Shunpeng Yang, Ben Liu, Hua Chen

展开摘要

Among on-policy reinforcement learning algorithms, Proximal Policy Optimization (PPO) demonstrates is widely favored for its simplicity, numerical stability, and strong empirical performance. Standard PPO relies on surrogate objectives defined via importance ratios, which require evaluating policy likelihood that is typically straightforward when the policy is modeled as a Gaussian distribution. However, extending PPO to more expressive, high-capacity policy models such as continuous normalizing flows (CNFs), also known as flow-matching models, is challenging because likelihood evaluation along the full flow trajectory is computationally expensive and often numerically unstable. To resolve this issue, we propose PolicyFlow, a novel on-policy CNF-based reinforcement learning algorithm that integrates expressive CNF policies with PPO-style objectives without requiring likelihood evaluation along the full flow path. PolicyFlow approximates importance ratios using velocity field variations along a simple interpolation path, reducing computational overhead without compromising training stability. To further prevent mode collapse and further encourage diverse behaviors, we propose the Brownian Regularizer, an implicit policy entropy regularizer inspired by Brownian motion, which is conceptually elegant and computationally lightweight. Experiments on diverse tasks across vairous environments including MultiGoal, PointMaze, IsaacLab and MuJoCo Playground show that PolicyFlow achieves competitive or superior performance compared to PPO using Gaussian policies and flow-based baselines including FPO and DPPO. Notably, results on MultiGoal highlight PolicyFlow’s ability to capture richer multimodal action distributions.

Poster
ConvRec-R1: Training LLM-based Conversational Recommender Systems with Reinforcement Learning

Yaochen Zhu, Harald Steck, Dawen Liang, Yinhan He, Vito Claudio Ostuni, Jundong Li, Nathan Kallus

展开摘要

Large language models (LLMs) are reshaping the recommender system paradigm by enabling users to express preferences and receive recommendations through conversations. Yet, aligning LLMs to the recommendation task remains challenging: pretrained LLMs often generate out-of-catalog items, violate required output formats, and their ranking quality degrades sharply toward the end of the generated list. To this end, we propose ConvRec-R1, a two-stage framework for end-to-end training of LLM-based conversational recommender systems. In Stage 1, we construct a behavioral-cloning dataset with a Remap-Reflect-Adjust pipeline, which produces high-quality, catalog-grounded demonstrations from powerful blackbox LLMs to warm-start the RL training. In Stage 2, we propose Rank-GRPO, a principled extension of group relative policy optimization (GRPO) tailored to tasks with rank-style outputs. Rank-GRPO treats each rank in the recommendation list as the unit instead of token (too fine-grained) or sequence (too coarse), redefining rewards to remove non-causal credit assignment and introducing a rank-level importance ratio based on the geometric mean of rank-wise token probabilities to stabilize policy updates. Experiments on the public Reddit-v2 dataset show that ConvRec-R1 converges faster and achieves higher Recall and NDCG than GRPO-style baselines. Code and datasets are released at https://anonymous.4open.science/r/ConvRec-R1-5615.

Poster
Transitive RL: Value Learning via Divide and Conquer

Seohong Park, Aditya Oberai, Pranav Atreya, Sergey Levine

展开摘要

In this work, we present Transitive Reinforcement Learning (TRL), a new value learning algorithm based on a divide-and-conquer paradigm. TRL is designed for offline goal-conditioned reinforcement learning (GCRL) problems, where the aim is to find a policy that can reach any state from any other state in the smallest number of steps. TRL converts a triangle inequality structure present in GCRL into a practical divide-and-conquer value update rule. This has several advantages compared to alternative value learning paradigms. Compared to temporal difference (TD) methods, TRL suffers less from bias accumulation, as in principle it only requires $O(\log T)$ recursions (as opposed to $O(T)$ in TD learning) to handle a length-T trajectory. Unlike Monte Carlo methods, TRL suffers less from high variance as it performs dynamic programming. Experimentally, we show that TRL achieves the best performance in highly challenging, long-horizon benchmark tasks compared to previous offline GCRL algorithms.

Poster
TROLL: Trust Regions Improve Reinforcement Learning for Large Language Models

Philipp Becker, Niklas Freymuth, Serge Thilges, Fabian Otto, Gerhard Neumann

展开摘要

Reinforcement Learning (RL) with PPO-like clip objectives has become the standard choice for reward-based fine-tuning of large language models (LLMs). Although recent work has explored improved estimators of advantages and normalization, the clipping mechanism itself has remained untouched. Originally introduced as a proxy for principled KL-based trust regions, clipping is a crude approximation that often causes unstable updates and suboptimal performance. We replace the clip objective with a novel discrete differentiable trust region projection, which provides principled token-level KL constraints. The projection operates on a sparse subset of the model’s most important token logits to balance computational cost and projection effectiveness. Our approach, Trust Region Optimization for Large Language Models (TROLL), serves as a direct replacement for PPO-like clipping during training and does not alter the model’s inference behavior. Across mathematical reasoning and code generation tasks, model families, as well as advantage-estimation methods, TROLL consistently outperforms PPO-like clipping in terms of training speed, stability, and final success rates.

Oral
Scalable Offline Model-Based RL with Action Chunks

Kwanyoung Park, Seohong Park, Youngwoon Lee, Sergey Levine

展开摘要

In this paper, we study whether model-based reinforcement learning (RL), in particular model-based value expansion, can provide a scalable recipe for tackling complex, long-horizon tasks in offline RL. Model-based value expansion fits an on-policy value function using length-$n$ imaginary rollouts generated by the current policy and a learned dynamics model. While larger $n$ reduces bias in value bootstrapping, it amplifies accumulated model errors over long horizons, degrading future predictions. We address this trade-off with an *action-chunk* model that predicts a future state from a sequence of actions (an "action chunk") instead of a single action, which reduces compounding errors. In addition, instead of directly training a policy to maximize rewards, we employ rejection sampling from an expressive behavioral action-chunk policy, which prevents model exploitation from out-of-distribution actions. We call this recipe **Model-Based RL with Action Chunks (MAC)**. Through experiments on highly challenging tasks with large-scale datasets of up to $100$M transitions, we show that MAC achieves the best performance among offline model-based RL algorithms, especially on challenging long-horizon tasks.

Poster
Causal Imitation Learning under Expert-Observable and Expert-Unobservable Confounding

Daqian Shao, Thomas Kleine Buening, Marta Kwiatkowska

展开摘要

We propose a general framework for causal Imitation Learning (IL) with hidden confounders, which subsumes several existing settings. Our framework accounts for two types of hidden confounders: (a) variables observed by the expert but not by the imitator, and (b) confounding noise hidden from both. By leveraging trajectory histories as instruments, we reformulate causal IL in our framework into a Conditional Moment Restriction (CMR) problem. We propose DML-IL, an algorithm that solves this CMR problem via instrumental variable regression, and upper bound its imitation gap. Empirical evaluation on continuous state-action environments, including Mujoco tasks, demonstrates that DML-IL outperforms existing causal IL baselines.

Poster
Quantile Advantage Estimation for Entropy-Safe Reasoning

Junkang Wu, Kexin Huang, Jiancan Wu, An Zhang, Xiang Wang, Xiangnan He

展开摘要

Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean-baseline used in value-free RL (\eg GRPO/DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise $K$-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries ($p \le 1{-}K$) it reinforces rare successes, while on easy queries ($p > 1{-}K$) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower/upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned $K$, roughly 80\% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME'24/'25 and AMC'23. These results identify {baseline design}—rather than token-level heuristics—as the primary mechanism for scaling RLVR.

Poster
Graph-Theoretic Intrinsic Reward: Guiding RL with Effective Resistance

Jatin Chauhan, Shivam Bhardwaj, Aditya Saibewar, Aditya Ramesh, Sadbhavana Babar, Manohar Kaul

展开摘要

Exploration of dynamic environments with sparse rewards is a significant challenge in Reinforcement Learning, often leading to inefficient exploration and brittle policies. To address this, we introduce a novel graph-based intrinsic reward using Effective Resistance, a metric from spectral graph theory. This reward formulation guides the agent to seek configurations that are directly correlated to successful goal reaching states. We provide theoretical guarantees, proving that our method not only learns a robust policy but also achieves faster convergence by serving as a variance reduction baseline to the standard discounted reward formulation. We perform extensive empirical analysis across several challenging environments to demonstrate that our approach significantly outperforms state-of-the-art baselines, demonstrating improvements of up to 59% in success rate, 56% in timesteps taken to reach the goal, and 4 times more accumulated reward. We augment all of the supporting lemmas and theoretically motivated hyperparameter choices with corresponding experiments.

Poster