Sicun Gao

Xiaofan Yu, Yunhui Guo, Sicun Gao et al.

Unsupervised lifelong learning refers to the ability to learn over time while memorizing previous patterns without supervision. Although great progress has been made in this direction, existing work often assumes strong prior knowledge about the incoming data (e.g., knowing the class boundaries), which can be impossible to obtain in complex and unpredictable environments. In this paper, motivated by real-world scenarios, we propose a more practical problem setting called online self-supervised lifelong learning without prior knowledge. The proposed setting is challenging due to the non-iid and single-pass data, the absence of external supervision, and no prior knowledge. To address the challenges, we propose Self-Supervised ContrAstive Lifelong LEarning without Prior Knowledge (SCALE) which can extract and memorize representations on the fly purely from the data continuum. SCALE is designed around three major components: a pseudo-supervised contrastive loss, a self-supervised forgetting loss, and an online memory update for uniform subset selection. All three components are designed to work collaboratively to maximize learning performance. We perform comprehensive experiments of SCALE under iid and four non-iid data streams. The results show that SCALE outperforms the state-of-the-art algorithm in all settings with improvements up to 3.83%, 2.77% and 5.86% in terms of kNN accuracy on CIFAR-10, CIFAR-100, and TinyImageNet datasets.

Chenning Yu, Sicun Gao

Sampling-based motion planning is a popular approach in robotics for finding paths in continuous configuration spaces. Checking collision with obstacles is the major computational bottleneck in this process. We propose new learning-based methods for reducing collision checking to accelerate motion planning by training graph neural networks (GNNs) that perform path exploration and path smoothing. Given random geometric graphs (RGGs) generated from batch sampling, the path exploration component iteratively predicts collision-free edges to prioritize their exploration. The path smoothing component then optimizes paths obtained from the exploration stage. The methods benefit from the ability of GNNs of capturing geometric patterns from RGGs through batch sampling and generalize better to unseen environments. Experimental results show that the learned components can significantly reduce collision checking and improve overall planning efficiency in challenging high-dimensional motion planning tasks.

Milan Ganai, Zheng Gong, Chenning Yu et al.

Ensuring safety is important for the practical deployment of reinforcement learning (RL). Various challenges must be addressed, such as handling stochasticity in the environments, providing rigorous guarantees of persistent state-wise safety satisfaction, and avoiding overly conservative behaviors that sacrifice performance. We propose a new framework, Reachability Estimation for Safe Policy Optimization (RESPO), for safety-constrained RL in general stochastic settings. In the feasible set where there exist violation-free policies, we optimize for rewards while maintaining persistent safety. Outside this feasible set, our optimization produces the safest behavior by guaranteeing entrance into the feasible set whenever possible with the least cumulative discounted violations. We introduce a class of algorithms using our novel reachability estimation function to optimize in our proposed framework and in similar frameworks such as those concurrently handling multiple hard and soft constraints. We theoretically establish that our algorithms almost surely converge to locally optimal policies of our safe optimization framework. We evaluate the proposed methods on a diverse suite of safe RL environments from Safety Gym, PyBullet, and MuJoCo, and show the benefits in improving both reward performance and safety compared with state-of-the-art baselines.

Chenning Yu, Hongzhan Yu, Sicun Gao

Deep reinforcement learning in continuous domains focuses on learning control policies that map states to distributions over actions that ideally concentrate on the optimal choices in each step. In multi-agent navigation problems, the optimal actions depend heavily on the agents' density. Their interaction patterns grow exponentially with respect to such density, making it hard for learning-based methods to generalize. We propose to switch the learning objectives from predicting the optimal actions to predicting sets of admissible actions, which we call control admissibility models (CAMs), such that they can be easily composed and used for online inference for an arbitrary number of agents. We design CAMs using graph neural networks and develop training methods that optimize the CAMs in the standard model-free setting, with the additional benefit of eliminating the need for reward engineering typically required to balance collision avoidance and goal-reaching requirements. We evaluate the proposed approach in multi-agent navigation environments. We show that the CAM models can be trained in environments with only a few agents and be easily composed for deployment in dense environments with hundreds of agents, achieving better performance than state-of-the-art methods.

Ruipeng Zhang, Chenning Yu, Jingkai Chen et al.

Learning-based methods have shown promising performance for accelerating motion planning, but mostly in the setting of static environments. For the more challenging problem of planning in dynamic environments, such as multi-arm assembly tasks and human-robot interaction, motion planners need to consider the trajectories of the dynamic obstacles and reason about temporal-spatial interactions in very large state spaces. We propose a GNN-based approach that uses temporal encoding and imitation learning with data aggregation for learning both the embeddings and the edge prioritization policies. Experiments show that the proposed methods can significantly accelerate online planning over state-of-the-art complete dynamic planning algorithms. The learned models can often reduce costly collision checking operations by more than 1000x, and thus accelerating planning by up to 95%, while achieving high success rates on hard instances as well.

Hongzhan Yu, Chiaki Hirayama, Chenning Yu et al.

There are two major challenges for scaling up robot navigation around dynamic obstacles: the complex interaction dynamics of the obstacles can be hard to model analytically, and the complexity of planning and control grows exponentially in the number of obstacles. Data-driven and learning-based methods are thus particularly valuable in this context. However, data-driven methods are sensitive to distribution drift, making it hard to train and generalize learned models across different obstacle densities. We propose a novel method for compositional learning of Sequential Neural Control Barrier models (SNCBFs) to achieve scalability. Our approach exploits an important observation: the spatial interaction patterns of multiple dynamic obstacles can be decomposed and predicted through temporal sequences of states for each obstacle. Through decomposition, we can generalize control policies trained only with a small number of obstacles, to environments where the obstacle density can be 100x higher. We demonstrate the benefits of the proposed methods in improving dynamic collision avoidance in comparison with existing methods including potential fields, end-to-end reinforcement learning, and model-predictive control. We also perform hardware experiments and show the practical effectiveness of the approach in the supplementary video.

Eric Yang Yu, Zhizhen Qin, Min Kyung Lee et al.

Long-term fairness is an important factor of consideration in designing and deploying learning-based decision systems in high-stake decision-making contexts. Recent work has proposed the use of Markov Decision Processes (MDPs) to formulate decision-making with long-term fairness requirements in dynamically changing environments, and demonstrated major challenges in directly deploying heuristic and rule-based policies that worked well in static environments. We show that policy optimization methods from deep reinforcement learning can be used to find strictly better decision policies that can often achieve both higher overall utility and less violation of the fairness requirements, compared to previously-known strategies. In particular, we propose new methods for imposing fairness requirements in policy optimization by regularizing the advantage evaluation of different actions. Our proposed methods make it easy to impose fairness constraints without reward engineering or sacrificing training efficiency. We perform detailed analyses in three established case studies, including attention allocation in incident monitoring, bank loan approval, and vaccine distribution in population networks.

Hui Shi, Yupeng Gu, Yitong Zhou et al.

User embeddings (vectorized representations of a user) are essential in recommendation systems. Numerous approaches have been proposed to construct a representation for the user in order to find similar items for retrieval tasks, and they have been proven effective in industrial recommendation systems as well. Recently people have discovered the power of using multiple embeddings to represent a user, with the hope that each embedding represents the user's interest in a certain topic. With multi-interest representation, it's important to model the user's preference over the different topics and how the preference change with time. However, existing approaches either fail to estimate the user's affinity to each interest or unreasonably assume every interest of every user fades with an equal rate with time, thus hurting the recall of candidate retrieval. In this paper, we propose the Multi-Interest Preference (MIP) model, an approach that not only produces multi-interest for users by using the user's sequential engagement more effectively but also automatically learns a set of weights to represent the preference over each embedding so that the candidates can be retrieved from each interest proportionally. Extensive experiments have been done on various industrial-scale datasets to demonstrate the effectiveness of our approach.

Chenning Yu, Qingbiao Li, Sicun Gao et al.

Conflict-Based Search is one of the most popular methods for multi-agent path finding. Though it is complete and optimal, it does not scale well. Recent works have been proposed to accelerate it by introducing various heuristics. However, whether these heuristics can apply to non-grid-based problem settings while maintaining their effectiveness remains an open question. In this work, we find that the answer is prone to be no. To this end, we propose a learning-based component, i.e., the Graph Transformer, as a heuristic function to accelerate the planning. The proposed method is provably complete and bounded-suboptimal with any desired factor. We conduct extensive experiments on two environments with dense graphs. Results show that the proposed Graph Transformer can be trained in problem instances with relatively few agents and generalizes well to a larger number of agents, while achieving better performance than state-of-the-art methods.

Yaoguang Zhai, Sicun Gao

The key to Black-Box Optimization is to efficiently search through input regions with potentially widely-varying numerical properties, to achieve low-regret descent and fast progress toward the optima. Monte Carlo Tree Search (MCTS) methods have recently been introduced to improve Bayesian optimization by computing better partitioning of the search space that balances exploration and exploitation. Extending this promising framework, we study how to further integrate sample-based descent for faster optimization. We design novel ways of expanding Monte Carlo search trees, with new descent methods at vertices that incorporate stochastic search and Gaussian Processes. We propose the corresponding rules for balancing progress and uncertainty, branch selection, tree expansion, and backpropagation. The designed search process puts more emphasis on sampling for faster descent and uses localized Gaussian Processes as auxiliary metrics for both exploitation and exploration. We show empirically that the proposed algorithms can outperform state-of-the-art methods on many challenging benchmark problems.

Sicun Gao

Logic is playing an increasingly important role in the engineering of real-time, hybrid, and cyber-physical systems, but mostly in the form of posterior verification and high-level analysis. The core methodology in the design of real-world systems consists mainly of control theory and numerical analysis, and has remained mostly free of logic and formal approaches. As a result, besides facing extreme difficulty in guaranteeing the reliability of these systems, engineers are also missing out the computational power of logic-based methods that has greatly advanced in the past decades. To change this situation, we need a logical and computational foundation for control theory. The name "descriptive control theory" emphasizes the overarching theme of using logic to express, analyze, and solve problems in control theory. If the program is successfully carried out, logical approaches will significantly extend existing engineering methods towards a unified methodology for handling nonlinear and hybrid systems, and bring design automation and reliability to an unprecedented level in the broad field of engineering.

Milan Ganai, Sicun Gao, Sylvia Herbert

Recent literature has proposed approaches that learn control policies with high performance while maintaining safety guarantees. Synthesizing Hamilton-Jacobi (HJ) reachable sets has become an effective tool for verifying safety and supervising the training of reinforcement learning-based control policies for complex, high-dimensional systems. Previously, HJ reachability was restricted to verifying low-dimensional dynamical systems primarily because the computational complexity of the dynamic programming approach it relied on grows exponentially with the number of system states. In recent years, a litany of proposed methods addresses this limitation by computing the reachability value function simultaneously with learning control policies to scale HJ reachability analysis while still maintaining a reliable estimate of the true reachable set. These HJ reachability approximations are used to improve the safety, and even reward performance, of learned control policies and can solve challenging tasks such as those with dynamic obstacles and/or with lidar-based or vision-based observations. In this survey paper, we review the recent developments in the field of HJ reachability estimation in reinforcement learning that would provide a foundational basis for further research into reliability in high-dimensional systems.

Tao Wang, Sylvia Herbert, Sicun Gao

Policy gradient lies at the core of deep reinforcement learning (RL) in continuous domains. Despite much success, it is often observed in practice that RL training with policy gradient can fail for many reasons, even on standard control problems with known solutions. We propose a framework for understanding one inherent limitation of the policy gradient approach: the optimization landscape in the policy space can be extremely non-smooth or fractal for certain classes of MDPs, such that there does not exist gradient to be estimated in the first place. We draw on techniques from chaos theory and non-smooth analysis, and analyze the maximal Lyapunov exponents and Hölder exponents of the policy optimization objectives. Moreover, we develop a practical method that can estimate the local smoothness of objective function from samples to identify when the training process has encountered fractal landscapes. We show experiments to illustrate how some failure cases of policy optimization can be explained by such fractal landscapes.

Nishit V. Pandya, Andrey Labunets, Sicun Gao et al.

A popular class of defenses against prompt injection attacks on large language models (LLMs) relies on fine-tuning the model to separate instructions and data, so that the LLM does not follow instructions that might be present with data. There are several academic systems and production-level implementations of this idea. We evaluate the robustness of this class of prompt injection defenses in the whitebox setting by constructing strong optimization-based attacks and showing that the defenses do not provide the claimed security properties. Specifically, we construct a novel attention-based attack algorithm for text-based LLMs and apply it to two recent whitebox defenses SecAlign (CCS 2025) and StruQ (USENIX Security 2025), showing attacks with success rates of up to 70% with modest increase in attacker budget in terms of tokens. Our findings make fundamental progress towards understanding the robustness of prompt injection defenses in the whitebox setting. We release our code and attacks at https://github.com/nishitvp/better_opts_attacks

Yuexin Bian, Jie Feng, Tao Wang et al.

On-policy deep reinforcement learning remains a dominant paradigm for continuous control, yet standard implementations rely on Gaussian actors and relatively shallow MLP policies, often leading to brittle optimization when gradients are noisy and policy updates must be conservative. In this paper, we revisit policy representation as a first-class design choice for on-policy optimization. We study discretized categorical actors that represent each action dimension with a distribution over bins, yielding a policy objective that resembles a cross-entropy loss. Building on architectural advances from supervised learning, we further propose regularized actor networks, while keeping critic design fixed. Our results show that simply replacing the standard actor network with our discretized regularized actor yields consistent gains and achieve the state-of-the-art performance across diverse continuous-control benchmarks.

Chenning Yu, Sicun Gao

We introduce a novel resampling criterion using lift scores, for improving compositional generation in diffusion models. By leveraging the lift scores, we evaluate whether generated samples align with each single condition and then compose the results to determine whether the composed prompt is satisfied. Our key insight is that lift scores can be efficiently approximated using only the original diffusion model, requiring no additional training or external modules. We develop an optimized variant that achieves relatively lower computational overhead during inference while maintaining effectiveness. Through extensive experiments, we demonstrate that lift scores significantly improved the condition alignment for compositional generation across 2D synthetic data, CLEVR position tasks, and text-to-image synthesis. Our code is available at http://rainorangelemon.github.io/complift.

Mingxin Yu, Chenning Yu, M-Mahdi Naddaf-Sh et al.

Sampling-based motion planning methods for manipulators in crowded environments often suffer from expensive collision checking and high sampling complexity, which make them difficult to use in real time. To address this issue, we propose a new generalizable control barrier function (CBF)-based steering controller to reduce the number of samples needed in a sampling-based motion planner RRT. Our method combines the strength of CBF for real-time collision-avoidance control and RRT for long-horizon motion planning, by using CBF-induced neural controller (CBF-INC) to generate control signals that steer the system towards sampled configurations by RRT. CBF-INC is learned as Neural Networks and has two variants handling different inputs, respectively: state (signed distance) input and point-cloud input from LiDAR. In the latter case, we also study two different settings: fully and partially observed environmental information. Compared to manually crafted CBF which suffers from over-approximating robot geometry, CBF-INC can balance safety and goal-reaching better without being over-conservative. Given state-based input, our neural CBF-induced neural controller-enhanced RRT (CBF-INC-RRT) can increase the success rate by 14% while reducing the number of nodes explored by 30%, compared with vanilla RRT on hard test cases. Given LiDAR input where vanilla RRT is not directly applicable, we demonstrate that our CBF-INC-RRT can improve the success rate by 10%, compared with planning with other steering controllers. Our project page with supplementary material is at https://mit-realm.github.io/CBF-INC-RRT-website/.

Hongzhan Yu, Seth Farrell, Ryo Yoshimitsu et al.

Learning-based methods for constructing control barrier functions (CBFs) are gaining popularity for ensuring safe robot control. A major limitation of existing methods is their reliance on extensive sampling over the state space or online system interaction in simulation. In this work we propose a novel framework for learning neural CBFs through a fixed, sparsely-labeled dataset collected prior to training. Our approach introduces new annotation techniques based on out-of-distribution analysis, enabling efficient knowledge propagation from the limited labeled data to the unlabeled data. We also eliminate the dependency on a high-performance expert controller, and allow multiple sub-optimal policies or even manual control during data collection. We evaluate the proposed method on real-world platforms. With limited amount of offline data, it achieves state-of-the-art performance for dynamic obstacle avoidance, demonstrating statistically safer and less conservative maneuvers compared to existing methods.

Ruipeng Zhang, Ya-Chien Chang, Sicun Gao

The Maximum Entropy Reinforcement Learning (MaxEnt RL) framework is a leading approach for achieving efficient learning and robust performance across many RL tasks. However, MaxEnt methods have also been shown to struggle with performance-critical control problems in practice, where non-MaxEnt algorithms can successfully learn. In this work, we analyze how the trade-off between robustness and optimality affects the performance of MaxEnt algorithms in complex control tasks: while entropy maximization enhances exploration and robustness, it can also mislead policy optimization, leading to failure in tasks that require precise, low-entropy policies. Through experiments on a variety of control problems, we concretely demonstrate this misleading effect. Our analysis leads to better understanding of how to balance reward design and entropy maximization in challenging control problems.

Tao Wang, Ruipeng Zhang, Sicun Gao

Modern policy gradient algorithms, such as TRPO and PPO, outperform vanilla policy gradient in many RL tasks. Questioning the common belief that enforcing approximate trust regions leads to steady policy improvement in practice, we show that the more critical factor is the enhanced value estimation accuracy from more value update steps in each iteration. To demonstrate, we show that by simply increasing the number of value update steps per iteration, vanilla policy gradient itself can achieve performance comparable to or better than PPO in all the standard continuous control benchmark environments. Importantly, this simple change to vanilla policy gradient is significantly more robust to hyperparameter choices, opening up the possibility that RL algorithms may still become more effective and easier to use.

Tao Wang, Bo Zhao, Sicun Gao et al.

Physics-Informed Neural Networks (PINNs) have gained popularity in scientific computing in recent years. However, they often fail to achieve the same level of accuracy as classical methods in solving differential equations. In this paper, we identify two sources of this issue in the case of Cauchy problems: the use of $L^2$ residuals as objective functions and the approximation gap of neural networks. We show that minimizing the sum of $L^2$ residual and initial condition error is not sufficient to guarantee the true solution, as this loss function does not capture the underlying dynamics. Additionally, neural networks are not capable of capturing singularities in the solutions due to the non-compactness of their image sets. This, in turn, influences the existence of global minima and the regularity of the network. We demonstrate that when the global minimum does not exist, machine precision becomes the predominant source of achievable error in practice. We also present numerical experiments in support of our theoretical claims.

Luobin Wang, Hongzhan Yu, Chenning Yu et al.

Diffusion models have recently gained significant attention in robotics due to their ability to generate multi-modal distributions of system states and behaviors. However, a key challenge remains: ensuring precise control over the generated outcomes without compromising realism. This is crucial for applications such as motion planning or trajectory forecasting, where adherence to physical constraints and task-specific objectives is essential. We propose a novel framework that enhances controllability in diffusion models by leveraging multi-modal prior distributions and enforcing strong modal coupling. This allows us to initiate the denoising process directly from distinct prior modes that correspond to different possible system behaviors, ensuring sampling to align with the training distribution. We evaluate our approach on motion prediction using the Waymo dataset and multi-task control in Maze2D environments. Experimental results show that our framework outperforms both guidance-based techniques and conditioned models with unimodal priors, achieving superior fidelity, diversity, and controllability, even in the absence of explicit conditioning. Overall, our approach provides a more reliable and scalable solution for controllable motion generation in robotics.

Ruipeng Zhang, Hongzhan Yu, Ya-Chien Chang et al.

Quadruped locomotion provides a natural setting for understanding when model-free learning can outperform model-based control design, by exploiting data patterns to bypass the difficulty of optimizing over discrete contacts and the combinatorial explosion of mode changes. We give a principled analysis of why imitation learning with quadrupeds can be inherently effective in a small data regime, based on the structure of its limit cycles, Poincaré return maps, and local numerical properties of neural networks. The understanding motivates a new imitation learning method that regulates the alignment between variations in a latent space and those over the output actions. Hardware experiments confirm that a few seconds of demonstration is sufficient to train various locomotion policies from scratch entirely offline with reasonable robustness.

Seth Farrell, Chenghao Li, Hongzhan Yu et al.

The integration of autonomous mobile robots (AMRs) in industrial environments, particularly warehouses, has revolutionized logistics and operational efficiency. However, ensuring the safety of human workers in dynamic, shared spaces remains a critical challenge. This work proposes a novel methodology that leverages control barrier functions (CBFs) to enhance safety in warehouse navigation. By integrating learning-based CBFs with the Open Robotics Middleware Framework (OpenRMF), the system achieves adaptive and safety-enhanced controls in multi-robot, multi-agent scenarios. Experiments conducted using various robot platforms demonstrate the efficacy of the proposed approach in avoiding static and dynamic obstacles, including human pedestrians. Our experiments evaluate different scenarios in which the number of robots, robot platforms, speed, and number of obstacles are varied, from which we achieve promising performance.

Chung-En Sun, Sicun Gao, Tsui-Wei Weng

Robustness remains a paramount concern in deep reinforcement learning (DRL), with randomized smoothing emerging as a key technique for enhancing this attribute. However, a notable gap exists in the performance of current smoothed DRL agents, often characterized by significantly low clean rewards and weak robustness. In response to this challenge, our study introduces innovative algorithms aimed at training effective smoothed robust DRL agents. We propose S-DQN and S-PPO, novel approaches that demonstrate remarkable improvements in clean rewards, empirical robustness, and robustness guarantee across standard RL benchmarks. Notably, our S-DQN and S-PPO agents not only significantly outperform existing smoothed agents by an average factor of $2.16\times$ under the strongest attack, but also surpass previous robustly-trained agents by an average factor of $2.13\times$. This represents a significant leap forward in the field. Furthermore, we introduce Smoothed Attack, which is $1.89\times$ more effective in decreasing the rewards of smoothed agents than existing adversarial attacks.

Hongzhan Yu, Sicun Gao

We present a new approach for input optimization of ReLU networks that explicitly takes into account the effect of changes in activation patterns. We analyze local optimization steps in both the input space and the space of activation patterns to propose methods with superior local descent properties. To accomplish this, we convert the discrete space of activation patterns into differentiable representations and propose regularization terms that improve each descent step. Our experiments demonstrate the effectiveness of the proposed input-optimization methods for improving the state-of-the-art in various areas, such as adversarial learning, generative modeling, and reinforcement learning.

Ya-Chien Chang, Sicun Gao

Reinforcement learning for control over continuous spaces typically uses high-entropy stochastic policies, such as Gaussian distributions, for local exploration and estimating policy gradient to optimize performance. Many robotic control problems deal with complex unstable dynamics, where applying actions that are off the feasible control manifolds can quickly lead to undesirable divergence. In such cases, most samples taken from the ambient action space generate low-value trajectories that hardly contribute to policy improvement, resulting in slow or failed learning. We propose to improve action selection in this model-free RL setting by introducing additional adaptive control steps based on Extremum-Seeking Control (ESC). On each action sampled from stochastic policies, we apply sinusoidal perturbations and query for estimated Q-values as the response signal. Based on ESC, we then dynamically improve the sampled actions to be closer to nearby optima before applying them to the environment. Our methods can be easily added in standard policy optimization to improve learning efficiency, which we demonstrate in various control learning environments.

Yaoguang Zhai, Zhizhen Qin, Sicun Gao

Standard approaches for global optimization of non-convex functions, such as branch-and-bound, maintain partition trees to systematically prune the domain. The tree size grows exponentially in the number of dimensions. We propose new sampling-based methods for non-convex optimization that adapts Monte Carlo Tree Search (MCTS) to improve efficiency. Instead of the standard use of visitation count in Upper Confidence Bounds, we utilize numerical overapproximations of the objective as an uncertainty metric, and also take into account of sampled estimates of first-order and second-order information. The Monte Carlo tree in our approach avoids the usual fixed combinatorial patterns in growing the tree, and aggressively zooms into the promising regions, while still balancing exploration and exploitation. We evaluate the proposed algorithms on high-dimensional non-convex optimization benchmarks against competitive baselines and analyze the effects of the hyper parameters.

Niloofar Mireshghallah, Justus Mattern, Sicun Gao et al.

With the advent of fluent generative language models that can produce convincing utterances very similar to those written by humans, distinguishing whether a piece of text is machine-generated or human-written becomes more challenging and more important, as such models could be used to spread misinformation, fake news, fake reviews and to mimic certain authors and figures. To this end, there have been a slew of methods proposed to detect machine-generated text. Most of these methods need access to the logits of the target model or need the ability to sample from the target. One such black-box detection method relies on the observation that generated text is locally optimal under the likelihood function of the generator, while human-written text is not. We find that overall, smaller and partially-trained models are better universal text detectors: they can more precisely detect text generated from both small and larger models. Interestingly, we find that whether the detector and generator were trained on the same data is not critically important to the detection success. For instance the OPT-125M model has an AUC of 0.81 in detecting ChatGPT generations, whereas a larger model from the GPT family, GPTJ-6B, has AUC of 0.45.

Charles Dawson, Sicun Gao, Chuchu Fan

Learning-enabled control systems have demonstrated impressive empirical performance on challenging control problems in robotics, but this performance comes at the cost of reduced transparency and lack of guarantees on the safety or stability of the learned controllers. In recent years, new techniques have emerged to provide these guarantees by learning certificates alongside control policies -- these certificates provide concise, data-driven proofs that guarantee the safety and stability of the learned control system. These methods not only allow the user to verify the safety of a learned controller but also provide supervision during training, allowing safety and stability requirements to influence the training process itself. In this paper, we provide a comprehensive survey of this rapidly developing field of certificate learning. We hope that this paper will serve as an accessible introduction to the theory and practice of certificate learning, both to those who wish to apply these tools to practical robotics problems and to those who wish to dive more deeply into the theory of learning for control.

Hui Shi, Sicun Gao, Yuandong Tian et al.

Long Short-Term Memory (LSTM) and Transformers are two popular neural architectures used for natural language processing tasks. Theoretical results show that both are Turing-complete and can represent any context-free language (CFL).In practice, it is often observed that Transformer models have better representation power than LSTM. But the reason is barely understood. We study such practical differences between LSTM and Transformer and propose an explanation based on their latent space decomposition patterns. To achieve this goal, we introduce an oracle training paradigm, which forces the decomposition of the latent representation of LSTM and the Transformer and supervises with the transitions of the Pushdown Automaton (PDA) of the corresponding CFL. With the forced decomposition, we show that the performance upper bounds of LSTM and Transformer in learning CFL are close: both of them can simulate a stack and perform stack operation along with state transitions. However, the absence of forced decomposition leads to the failure of LSTM models to capture the stack and stack operations, while having a marginal impact on the Transformer model. Lastly, we connect the experiment on the prototypical PDA to a real-world parsing task to re-verify the conclusions

Charles Dawson, Zengyi Qin, Sicun Gao et al.

Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models. We develop a model-based learning approach to synthesize robust feedback controllers with safety and stability guarantees. We take inspiration from robust convex optimization and Lyapunov theory to define robust control Lyapunov barrier functions that generalize despite model uncertainty. We demonstrate our approach in simulation on problems including car trajectory tracking, nonlinear control with obstacle avoidance, satellite rendezvous with safety constraints, and flight control with a learned ground effect model. Simulation results show that our approach yields controllers that match or exceed the capabilities of robust MPC while reducing computational costs by an order of magnitude.

Ya-Chien Chang, Sicun Gao

The lack of stability guarantee restricts the practical use of learning-based methods in core control problems in robotics. We develop new methods for learning neural control policies and neural Lyapunov critic functions in the model-free reinforcement learning (RL) setting. We use sample-based approaches and the Almost Lyapunov function conditions to estimate the region of attraction and invariance properties through the learned Lyapunov critic functions. The methods enhance stability of neural controllers for various nonlinear systems including automobile and quadrotor control.

Yuda Song, Aditi Mavalankar, Wen Sun et al.

The high sample complexity of reinforcement learning challenges its use in practice. A promising approach is to quickly adapt pre-trained policies to new environments. Existing methods for this policy adaptation problem typically rely on domain randomization and meta-learning, by sampling from some distribution of target environments during pre-training, and thus face difficulty on out-of-distribution target environments. We propose new model-based mechanisms that are able to make online adaptation in unseen target environments, by combining ideas from no-regret online learning and adaptive control. We prove that the approach learns policies in the target environment that can quickly recover trajectories from the source environment, and establish the rate of convergence in general settings. We demonstrate the benefits of our approach for policy adaptation in a diverse set of continuous control tasks, achieving the performance of state-of-the-art methods with much lower sample complexity.

Ya-Chien Chang, Nima Roohi, Sicun Gao

We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and Lyapunov functions, and a falsifier that finds counterexamples to quickly guide the learner towards solutions. The procedure terminates when no counterexample is found by the falsifier, in which case the controlled nonlinear system is provably stable. The approach significantly simplifies the process of Lyapunov control design, provides end-to-end correctness guarantee, and can obtain much larger regions of attraction than existing methods such as LQR and SOS/SDP. We show experiments on how the new methods obtain high-quality solutions for challenging control problems.

Quan Vuong, Sharad Vikram, Hao Su et al.

Recently, reinforcement learning (RL) algorithms have demonstrated remarkable success in learning complicated behaviors from minimally processed input. However, most of this success is limited to simulation. While there are promising successes in applying RL algorithms directly on real systems, their performance on more complex systems remains bottle-necked by the relative data inefficiency of RL algorithms. Domain randomization is a promising direction of research that has demonstrated impressive results using RL algorithms to control real robots. At a high level, domain randomization works by training a policy on a distribution of environmental conditions in simulation. If the environments are diverse enough, then the policy trained on this distribution will plausibly generalize to the real world. A human-specified design choice in domain randomization is the form and parameters of the distribution of simulated environments. It is unclear how to the best pick the form and parameters of this distribution and prior work uses hand-tuned distributions. This extended abstract demonstrates that the choice of the distribution plays a major role in the performance of the trained policies in the real world and that the parameter of this distribution can be optimized to maximize the performance of the trained policies in the real world

Jacek Cyranka, Md. Ariful Islam, Scott A. Smolka et al.

We introduce continuous Lagrangian reachability (CLRT), a new algorithm for the computation of a tight and continuous-time reachtube for the solution flows of a nonlinear, time-variant dynamical system. CLRT employs finite strain theory to determine the deformation of the solution set from time $t_i$ to time $t_{i+1}$. We have developed simple explicit analytic formulas for the optimal metric for this deformation; this is superior to prior work, which used semi-definite programming. CLRT also uses infinitesimal strain theory to derive an optimal time increment $h_i$ between $t_i$ and $t_{i+1}$, nonlinear optimization to minimally bloat (i.e., using a minimal radius) the state set at time $t_i$ such that it includes all the states of the solution flow in the interval $[t_i,t_{i+1}]$. We use $δ$-satisfiability to ensure the correctness of the bloating. Our results on a series of benchmarks show that CLRT performs favorably compared to state-of-the-art tools such as CAPD in terms of the continuous reachtube volumes they compute.

Jeevana Priya Inala, Sicun Gao, Soonho Kong et al.

In this paper, we present ReaS, a technique that combines numerical optimization with SAT solving to synthesize unknowns in a program that involves discrete and floating point computation. ReaS makes the program end-to-end differentiable by smoothing any Boolean expression that introduces discontinuity such as conditionals and relaxing the Boolean unknowns so that numerical optimization can be performed. On top of this, ReaS uses a SAT solver to help the numerical search overcome local solutions by incrementally fixing values to the Boolean expressions. We evaluated the approach on 5 case studies involving hybrid systems and show that ReaS can synthesize programs that could not be solved by previous SMT approaches.