SMART: Self-learning Meta-strategy Agent for Reasoning Tasks

Tasks requiring deductive reasoning, especially those involving multiple steps, often demand adaptive strategies such as intermediate generation of rationales or programs, as no single approach is universally optimal. While Language Models (LMs) can enhance their outputs through iterative self-refinement and strategy adjustments, they frequently fail to apply the most effective strategy in their first attempt. This inefficiency raises the question: Can LMs learn to select the optimal strategy in the first attempt, without a need for refinement? To address this challenge, we introduce SMART (Self-learning Meta-strategy Agent for Reasoning Tasks), a novel framework that enables LMs to autonomously learn and select the most effective strategies for various reasoning tasks. We model the strategy selection process as a Markov Decision Process and leverage reinforcement learning-driven continuous self-improvement to allow the model to find the suitable strategy to solve a given task. Unlike traditional self-refinement methods that rely on multiple inference passes or external feedback, SMART allows an LM to internalize the outcomes of its own reasoning processes and adjust its strategy accordingly, aiming for correct solutions on the first attempt. Our experiments across various reasoning datasets and with different model architectures demonstrate that SMART significantly enhances the ability of models to choose optimal strategies without external guidance (+15 points on the GSM8K dataset). By achieving higher accuracy with a single inference pass, SMART not only improves performance but also reduces computational costs for refinement-based strategies, paving the way for more efficient and intelligent reasoning in LMs.

Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming framework

Learning uncertain dynamics models using Gaussian process~(GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability, most approaches for Gaussian process-based model predictive control (GP-MPC) are based on approximations of the reachable set that are either overly conservative or impede the controller's safety guarantees. To address these challenges, we propose a robust GP-MPC formulation that guarantees constraint satisfaction with high probability. For its tractable implementation, we propose a sampling-based GP-MPC approach that iteratively generates consistent dynamics samples from the GP within a sequential quadratic programming framework. We highlight the improved reachable set approximation compared to existing methods, as well as real-time feasible computation times, using two numerical examples.

Global Reinforcement Learning: Beyond Linear and Convex Rewards via Submodular Semi-gradient Methods

In classic Reinforcement Learning (RL), the agent maximizes an additive objective of the visited states, e.g., a value function. Unfortunately, objectives of this type cannot model many real-world applications such as experiment design, exploration, imitation learning, and risk-averse RL to name a few. This is due to the fact that additive objectives disregard interactions between states that are crucial for certain tasks. To tackle this problem, we introduce Global RL (GRL), where rewards are globally defined over trajectories instead of locally over states. Global rewards can capture negative interactions among states, e.g., in exploration, via submodularity, positive interactions, e.g., synergetic effects, via supermodularity, while mixed interactions via combinations of them. By exploiting ideas from submodular optimization, we propose a novel algorithmic scheme that converts any GRL problem to a sequence of classic RL problems and solves it efficiently with curvature-dependent approximation guarantees. We also provide hardness of approximation results and empirically demonstrate the effectiveness of our method on several GRL instances.

Safe Guaranteed Exploration for Non-linear Systems

Safely exploring environments with a-priori unknown constraints is a fundamental challenge that restricts the autonomy of robots. While safety is paramount, guarantees on sufficient exploration are also crucial for ensuring autonomous task completion. To address these challenges, we propose a novel safe guaranteed exploration framework using optimal control, which achieves first-of-its-kind results: guaranteed exploration for non-linear systems with finite time sample complexity bounds, while being provably safe with arbitrarily high probability. The framework is general and applicable to many real-world scenarios with complex non-linear dynamics and unknown domains. Based on this framework we propose an efficient algorithm, SageMPC, SAfe Guaranteed Exploration using Model Predictive Control. SageMPC improves efficiency by incorporating three techniques: i) exploiting a Lipschitz bound, ii) goal-directed exploration, and iii) receding horizon style re-planning, all while maintaining the desired sample complexity, safety and exploration guarantees of the framework. Lastly, we demonstrate safe efficient exploration in challenging unknown environments using SageMPC with a car model.

Submodular Reinforcement Learning

In reinforcement learning (RL), rewards of states are typically considered additive, and following the Markov assumption, they are $\textit{independent}$ of states visited previously. In many important applications, such as coverage control, experiment design and informative path planning, rewards naturally have diminishing returns, i.e., their value decreases in light of similar states visited previously. To tackle this, we propose $\textit{submodular RL}$ (SubRL), a paradigm which seeks to optimize more general, non-additive (and history-dependent) rewards modelled via submodular set functions which capture diminishing returns. Unfortunately, in general, even in tabular settings, we show that the resulting optimization problem is hard to approximate. On the other hand, motivated by the success of greedy algorithms in classical submodular optimization, we propose SubPO, a simple policy gradient-based algorithm for SubRL that handles non-additive rewards by greedily maximizing marginal gains. Indeed, under some assumptions on the underlying Markov Decision Process (MDP), SubPO recovers optimal constant factor approximations of submodular bandits. Moreover, we derive a natural policy gradient approach for locally optimizing SubRL instances even in large state- and action- spaces. We showcase the versatility of our approach by applying SubPO to several applications, such as biodiversity monitoring, Bayesian experiment design, informative path planning, and coverage maximization. Our results demonstrate sample efficiency, as well as scalability to high-dimensional state-action spaces.

Near-Optimal Multi-Agent Learning for Safe Coverage Control

In multi-agent coverage control problems, agents navigate their environment to reach locations that maximize the coverage of some density. In practice, the density is rarely known $\textit{a priori}$, further complicating the original NP-hard problem. Moreover, in many applications, agents cannot visit arbitrary locations due to $\textit{a priori}$ unknown safety constraints. In this paper, we aim to efficiently learn the density to approximately solve the coverage problem while preserving the agents' safety. We first propose a conditionally linear submodular coverage function that facilitates theoretical analysis. Utilizing this structure, we develop MacOpt, a novel algorithm that efficiently trades off the exploration-exploitation dilemma due to partial observability, and show that it achieves sublinear regret. Next, we extend results on single-agent safe exploration to our multi-agent setting and propose SafeMac for safe coverage and exploration. We analyze SafeMac and give first of its kind results: near optimal coverage in finite time while provably guaranteeing safety. We extensively evaluate our algorithms on synthetic and real problems, including a bio-diversity monitoring task under safety constraints, where SafeMac outperforms competing methods.

Competitive Policy Optimization

A core challenge in policy optimization in competitive Markov decision processes is the design of efficient optimization methods with desirable convergence and stability properties. To tackle this, we propose competitive policy optimization (CoPO), a novel policy gradient approach that exploits the game-theoretic nature of competitive games to derive policy updates. Motivated by the competitive gradient optimization method, we derive a bilinear approximation of the game objective. In contrast, off-the-shelf policy gradient methods utilize only linear approximations, and hence do not capture interactions among the players. We instantiate CoPO in two ways:(i) competitive policy gradient, and (ii) trust-region competitive policy optimization. We theoretically study these methods, and empirically investigate their behavior on a set of comprehensive, yet challenging, competitive games. We observe that they provide stable optimization, convergence to sophisticated strategies, and higher scores when played against baseline policy gradient methods.

AMZ Driverless: The Full Autonomous Racing System

This paper presents the algorithms and system architecture of an autonomous racecar. The introduced vehicle is powered by a software stack designed for robustness, reliability, and extensibility. In order to autonomously race around a previously unknown track, the proposed solution combines state of the art techniques from different fields of robotics. Specifically, perception, estimation, and control are incorporated into one high-performance autonomous racecar. This complex robotic system, developed by AMZ Driverless and ETH Zurich, finished 1st overall at each competition we attended: Formula Student Germany 2017, Formula Student Italy 2018 and Formula Student Germany 2018. We discuss the findings and learnings from these competitions and present an experimental evaluation of each module of our solution.

Redundant Perception and State Estimation for Reliable Autonomous Racing

In autonomous racing, vehicles operate close to the limits of handling and a sensor failure can have critical consequences. To limit the impact of such failures, this paper presents the redundant perception and state estimation approaches developed for an autonomous race car. Redundancy in perception is achieved by estimating the color and position of the track delimiting objects using two sensor modalities independently. Specifically, learning-based approaches are used to generate color and pose estimates, from LiDAR and camera data respectively. The redundant perception inputs are fused by a particle filter based SLAM algorithm that operates in real-time. Velocity is estimated using slip dynamics, with reliability being ensured through a probabilistic failure detection algorithm. The sub-modules are extensively evaluated in real-world racing conditions using the autonomous race car "gotthard driverless", achieving lateral accelerations up to 1.7G and a top speed of 90km/h.