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.

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 github.com/rainorangelemon/complift.

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.

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.

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.

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. Our code is available at: https://github.com/Trustworthy-ML-Lab/Robust_HighUtil_Smoothed_DRL

Policy gradient methods have enabled deep reinforcement learning (RL) to approach challenging continuous control problems, even when the underlying systems involve highly nonlinear dynamics that generate complex non-smooth optimization landscapes. We develop a rigorous framework for understanding how policy gradient methods mollify non-smooth optimization landscapes to enable effective policy search, as well as the downside of it: while making the objective function smoother and easier to optimize, the stochastic objective deviates further from the original problem. We demonstrate the equivalence between policy gradient methods and solving backward heat equations. Following the ill-posedness of backward heat equations from PDE theory, we present a fundamental challenge to the use of policy gradient under stochasticity. Moreover, we make the connection between this limitation and the uncertainty principle in harmonic analysis to understand the effects of exploration with stochastic policies in RL. We also provide experimental results to illustrate both the positive and negative aspects of mollification effects in practice.

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.

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.

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 (CBFINC-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-INCRRT 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/CBFINC-RRT-website/.

Neural Control Barrier Functions (NCBFs) have shown significant promise in enforcing safety constraints on nonlinear autonomous systems. State-of-the-art exact approaches to verifying safety of NCBF-based controllers exploit the piecewise-linear structure of ReLU neural networks, however, such approaches still rely on enumerating all of the activation regions of the network near the safety boundary, thus incurring high computation cost. In this paper, we propose a framework for Synthesis with Efficient Exact Verification (SEEV). Our framework consists of two components, namely (i) an NCBF synthesis algorithm that introduces a novel regularizer to reduce the number of activation regions at the safety boundary, and (ii) a verification algorithm that exploits tight over-approximations of the safety conditions to reduce the cost of verifying each piecewise-linear segment. Our simulations show that SEEV significantly improves verification efficiency while maintaining the CBF quality across various benchmark systems and neural network structures. Our code is available at https://github.com/HongchaoZhang-HZ/SEEV.

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. 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 changes 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 at an equal rate with time, thus hurting the performance 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.

The deployment of Reinforcement Learning to robotics applications faces the difficulty of reward engineering. Therefore, approaches have focused on creating reward functions by Learning from Observations (LfO) which is the task of learning policies from expert trajectories that only contain state sequences. We propose new methods for LfO for the important class of continuous control problems of learning to stabilize, by introducing intermediate proxy models acting as reward functions between the expert and the agent policy based on Lyapunov stability theory. Our LfO training process consists of two steps. The first step attempts to learn a Lyapunov-like landscape proxy model from expert state sequences without access to any kinematics model, and the second step uses the learned landscape model to guide in training the learner's policy. We formulate novel learning objectives for the two steps that are important for overall training success. We evaluate our methods in real automobile robot environments and other simulated stabilization control problems in model-free settings, like Quadrotor control and maintaining upright positions of Hopper in MuJoCo. We compare with state-of-the-art approaches and show the proposed methods can learn efficiently with less expert observations.

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.

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 (SN-CBFs) 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.

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.

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 H\"older 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.

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 article, we provide a comprehensive survey of this rapidly developing field of certificate learning. We hope that this article 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.

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 LSTMand 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

Path-tracking control of self-driving vehicles can benefit from deep learning for tackling longstanding challenges such as nonlinearity and uncertainty. However, deep neural controllers lack safety guarantees, restricting their practical use. We propose a new approach of learning almost-barrier functions, which approximately characterizes the forward invariant set for the system under neural controllers, to quantitatively analyze the safety of deep neural controllers for path-tracking. We design sampling-based learning procedures for constructing candidate neural barrier functions, and certification procedures that utilize robustness analysis for neural networks to identify regions where the barrier conditions are fully satisfied. We use an adversarial training loop between learning and certification to optimize the almost-barrier functions. The learned barrier can also be used to construct online safety monitors through reachability analysis. We demonstrate effectiveness of our methods in quantifying safety of neural controllers in various simulation environments, ranging from simple kinematic models to the TORCS simulator with high-fidelity vehicle dynamics simulation.

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.

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.

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.

Artificial intelligence is increasingly being used to manage the workforce. Algorithmic management promises organizational efficiency, but often undermines worker well-being. How can we computationally model worker well-being so that algorithmic management can be optimized for and assessed in terms of worker well-being? Toward this goal, we propose a participatory approach for worker well-being models. We first define worker well-being models: Work preference models---preferences about work and working conditions, and managerial fairness models---beliefs about fair resource allocation among multiple workers. We then propose elicitation methods to enable workers to build their own well-being models leveraging pairwise comparisons and ranking. As a case study, we evaluate our methods in the context of algorithmic work scheduling with 25 shift workers and 3 managers. The findings show that workers expressed idiosyncratic work preference models and more uniform managerial fairness models, and the elicitation methods helped workers discover their preferences and gave them a sense of empowerment. Our work provides a method and initial evidence for enabling participatory algorithmic management for worker well-being.

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 modelfree 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.

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.

In this article, we propose an automated standard cell synthesis framework, SP&R, which simultaneously solves P&R without deploying any sequential/separate operations, by a novel dynamic pin allocation scheme. The proposed SP&R utilizes the multiobjective optimization feature of satisfiability modulo theories (SMT) to obtain optimal cell layouts. To achieve practical scalability of the framework, we develop various search-space reduction techniques, including breaking symmetry, conditional assignment/localization, and cell/objective function partitioning. Compared to the previous work, SP&R achieves 20.8× to 131.7× runtime improvements on average across the design-rule sets. As a result, SP&R successfully produces cell layouts up to 36 field-effect transistors (FETs) and 27 nets within 1.75 h by orchestrating all innovative tactics together, resulting in the generation of a whole 7-nm standard cell library. Compared to the known layouts, our work improves cell size and # M2 tracks by 0.1 contacted poly pitch and 0.3 tracks, respectively.

Standard cell synthesis requires careful engineering approaches to ensure routability across various digital IC designs since physical design (PD) for sub-7nm technology nodes demands holistic efforts to address urgent and nontrivial design challenges. The smaller number of routing tracks and more complex design rules due to the sophisticated multi-patterning technology make place-and-route (P&R) for designing a standard cell extremely hard and time-consuming. Many conventional approaches have been suggested for improving transistor-level P&R and pin accessibility, nonetheless insufficient because of the heuristic/divide-and-conquer manners. In this paper, we propose a novel framework, SP&R, which simultaneously solves P&R for designing standard cell's layout without deploying any sequential procedures (between place and route steps) by using dynamic pin allocation-based cell synthesis. The proposed SP&R utilizes the Optimization Modulo Theories (OMT), an extension of the Satisfiability modulo theories (SMT), to obtain optimal standard cell layout by virtue of SAT (Boolean Satisfiability)-based fast reasoning ability. We validate that our SP&R framework achieves 10.5% of reduction on average in terms of metal length compared to the sequential approach, through practical standard cell designs targeting sub-7nm technology nodes.

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. Our project website, including code, can be found at https://yudasong.github.io/PADA.

Pin accessibility encounters nontrivial challenges due to the smaller number of routing tracks, higher pin density, and more complex design rules. Consequently, securing design rule-correct routability has become a critical bottleneck for sub-10-nm IC designs (particularly in the detailed routing stage) costing days of runtime. To reduce turnaround time, IC designers demand new design methodologies to analyze the routing feasibility of a given layout architecture (e.g., conditional design rules, pin assignment patterns, etc). There are several conventional methods capable of assessing routability that consider pin accessibility. However, precise diagnosis of unroutable layouts remains an open problem for IC design practitioners. In this article, we propose two novel frameworks that: 1) efficiently analyzes design rule-correct routability via an integer linear programming (ILP)-derived Boolean satisfiability (SAT) formulation written in light-weight conjunctive normal form, on top of multicommodity flow theory and 2) precisely diagnose explicit reasons for design-rule violations (DRVs) in the form of human-interpretable explanations, while specifying conflicting design rules with a physical location. While covering a variety of conditional design rules, we have refined our formulation by using SAT encoding techniques, supernode simplification, Boolean constraint propagation-based preprocessing, etc. We demonstrate that our routability analysis framework produces design rule-correct routability assessment within 0.02% of ILP runtime on average. Also, our routability diagnosis framework precisely examines DRVs, revealing design-rule conflicts for a variety of pin layouts and switchboxes. We show our frameworks scalability by utilizing practical benchmarks ranging up to 40000 grid-size layouts (i.e., 200 Htrack × 200 Vtrack), producing results within an hour.

Neural networks in real-world applications have to satisfy critical properties such as safety and reliability. The analysis of such properties typically requires extracting information through computing pre-images of the network transformations, but it is well-known that explicit computation of pre-images is intractable. We introduce new methods for computing compact symbolic abstractions of pre-images by computing their overapproximations and underapproximations through all layers. The abstraction of pre-images enables formal analysis and knowledge extraction without affecting standard learning algorithms. We use inverse abstractions to automatically extract simple control laws and compact representations for pre-images corresponding to unsafe outputs. We illustrate that the extracted abstractions are interpretable and can be used for analyzing complex properties.

We formulate numerically-robust inductive proof rules for unbounded stability and safety properties of continuous dynamical systems. These induction rules robustify standard notions of Lyapunov functions and barrier certificates so that they can tolerate small numerical errors. In this way, numerically-driven decision procedures can establish a sound and relative-complete proof system for unbounded properties of very general nonlinear systems. We demonstrate the effectiveness of the proposed rules for rigorously verifying unbounded properties of various nonlinear systems, including a challenging powertrain control model.

We present VeriSketch, a security-oriented program synthesis framework for developing hardware designs with formal guarantee of functional and security specifications. VeriSketch defines a synthesis language, a code instrumentation framework for specifying and inferring timing-sensitive information flow properties, and uses specialized constraint-based synthesis for generating HDL code that enforces the specifications. We show the power of VeriSketch through security-critical hardware design examples, including cache controllers, thread schedulers, and system-on-chip arbiters, with formal guarantee of security properties such as absence of timing side-channels, confidentiality, and isolation.

Routability diagnosis has increasingly become the bottleneck in detailed routing for sub-10nm technology due to the limited tracks, high density, and complex design rules. The conventional ways to examine the routability of detailed routing are ILP- and SAT-based techniques. However, once we identify the routability, the diagnosis remains an open problem for physical designers. In this paper, we propose a novel framework, called ROAD, which diagnoses explicit reasons for routing failures. The proposed ROAD framework utilizes a diagnosis-friendly SAT formulation to represent design's layout and diagnoses the routability with SAT solving techniques. Based on the diagnosis, ROAD provides human-interpretable explanations for conflicted routing conditions. To show the practical value of our framework, we also generate comprehensive test-sets that enable exhaustive exploration of layouts based on Rent's rule. We demonstrate that ROAD successfully examines conflict causes for diverse pin layouts. Throughout extensive diagnosis, we also present several key findings for design failure. ROAD performs routability diagnosis within 2 minutes on average for 90 grids testsets, while diagnosing the exact causes of routing failures in terms of congestion and conditional design rules.

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 robot control problems such as path tracking for wheeled vehicles and humanoid robot balancing.

We propose $$\delta $$ -complete decision procedures for solving satisfiability of nonlinear SMT problems over real numbers that contain universal quantification and a wide range of nonlinear functions. The methods combine interval constraint propagation, counterexample-guided synthesis, and numerical optimization. In particular, we show how to handle the interleaving of numerical and symbolic computation to ensure delta-completeness in quantified reasoning. We demonstrate that the proposed algorithms can handle various challenging global optimization and control synthesis problems that are beyond the reach of existing solvers.

Approximate computing aims to trade accuracy for energy efficiency. Various approximate methods have been proposed in the literature that demonstrate the effectiveness of relaxing accuracy requirements in a specific unit. This provides a basis for exploring simultaneous use of multiple approximate units to improve efficiency under guarantees on quality of results. In this paper, we explore the effect of combining multiple approximate units on the energy consumption and identify the best setting that minimizes energy consumption under a quality constraint. Our approach also enables changes in unit configurations throughout the program. To do this effectively, we need a method to examine the combined impact of multiple approximate units on the output quality, and configure individual units accordingly. To solve this problem, we propose LEMAX that uses gradient descent approach to identify the best configuration of the individual approximate units for a given program. We evaluate the efficacy of LEMAX in minimizing the energy consumption of several machine learning applications with varying size (i.e., number of operations) under different quality constraints. Our evaluation shows that the configuration provided by LEMAX for a system with multiple approximate units improves the energy consumption by on average, 97.7%, 83.12%, and 73.95% for quality loss of 5%, 2% and 0.5%, respectively, compared to configurations obtained for a system with a single approximate resource.

We present SMT-based techniques for analyzing networks of nonlinear hybrid systems, which interact with each other in both discrete and continuous ways. We propose a modular encoding method to reduce reachability problems of hybrid components, involving continuous I/O as well as usual discrete I/O, into the satisfiability of first-order logic formulas over the real numbers. We identify a generic class of logical formulas to modularly encode networks of hybrid systems, and present an SMT algorithm for checking the satisfiability of such logical formulas. The experimental results show that our techniques significantly increase the performance of SMT-based analysis for networks of nonlinear hybrid components.

We propose a new abstraction refinement procedure based on machine learning to improve the performance of nonlinear constraint solving algorithms on large-scale problems. The proposed approach decomposes the original set of constraints into smaller subsets, and uses learning algorithms to propose sequences of abstractions that take the form of conjunctions of classifiers. The core procedure is a refinement loop that keeps improving the learned results based on counterexamples that are obtained from partial constraints that are easy to solve. Experiments show that the proposed techniques significantly improve the performance of state-of-the-art constraint solvers on many challenging benchmarks. The mechanism is capable of producing intermediate symbolic abstractions that are also important for many applications and for understanding the internal structures of hard constraint solving problems.

In this paper, we survey recent progress in CyberCardia project, a CPS Frontier project funded by the National Science Foundation. The CyberCardia project will lead to significant advances in the state of the art for system verification and cardiac therapies based on the use of formal methods and closed-loop control and verification. The animating vision for the work is to enable the development of a true in silico design methodology for medical devices that can be used to speed the development of new devices and to provide greater assurance that their behavior matches designer intentions, and to pass regulatory muster more quickly so that they can be used on patients needing their care. The acceleration in medical-device innovation achievable as a result of the CyberCardia research will also have long-term and sustained societal benefits, as better diagnostic and therapeutic technologies enter into the practice of medicine more quickly.

This paper presents general techniques for verifying virtually synchronous distributed control systems with interconnected physical environments. Such cyber-physical systems (CPSs) are notoriously hard to verify, due to their combination of nontrivial continuous dynamics, network delays, imprecise local clocks, asynchronous communication, etc. To simplify their analysis, we first extend the PALS methodology---that allows to abstract from the timing of events, asynchronous communication, network delays, and imprecise clocks, as long as the infrastructure guarantees bounds on the network delays and clock skews---from real-time to hybrid systems. We prove a bisimulation equivalence between Hybrid PALS synchronous and asynchronous models. We then show how various verification problems for synchronous Hybrid PALS models can be reduced to SMT solving over nonlinear theories of the real numbers. We illustrate the Hybrid PALS modeling and verification methodology on a number of CPSs, including a control system for turning an airplane.

PDDL+ planning involves reasoning about mixed discrete-continuous change over time. Nearly all PDDL+ planners assume that continuous change is linear. We present a new technique that accommodates nonlinear change by encoding problems as nonlinear hybrid systems. Using this encoding, we apply a Satisfiability Modulo Theories (SMT) solver to find plans. We show that it is important to use novel planning- specific heuristics for variable and value selection for SMT solving, which is inspired by recent advances in planning as SAT. We show the promising performance of the resulting solver on challenging nonlinear problems.

Recent clinical studies suggest that the efficacy of hormone therapy for prostate cancer depends on the characteristics of individual patients. In this paper, we develop a computational framework for identifying patient-specific androgen ablation therapy schedules for postponing the potential cancer relapse. We model the population dynamics of heterogeneous prostate cancer cells in response to androgen suppression as a nonlinear hybrid automaton. We estimate personalized kinetic parameters to characterize patients and employ δ-reachability analysis to predict patient-specific therapeutic strategies. The results show that our methods are promising and may lead to a prognostic tool for prostate cancer therapy.

Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any sentence A containing only bounded quantifiers and functions in F, and any positive rational number delta, decides either “A is true”, or “a delta-strengthening of A is false”. Moreover, if F can be computed in complexity class C, then under mild assumptions, this “delta-decision problem” for bounded Sigma k-sentences resides in Sigma k(C). The results stand in sharp contrast to the well-known undecidability of the general first-order theories with these functions, and serve as a theoretical basis for the use of numerical methods in decision procedures for formulas over the reals.