The foundation model enables general-purpose problem-solving and enjoys desirable rapid adaptation due to its adopted cross-task generalization paradigms, e.g., pretraining, meta-training, and finetuning. Recent advances in these paradigms show the crucial role of challenging tasks' prioritized sampling in enhancing adaptation robustness. However, ranking task difficulties exhausts massive task queries to evaluate, thus computation and annotation intensive, which is typically unaffordable in practice. This work underscores the criticality of both adaptation robustness and learning efficiency, especially in scenarios where tasks are risky or costly to evaluate, e.g., policy evaluations in Markov decision processes (MDPs) or inference with large models. To this end, we present Model Predictive Task Sampling (MPTS) to establish connections between the task space and adaptation risk landscape to form a theoretical guideline in robust active task sampling. MPTS characterizes the task episodic information with a generative model and directly predicts task-specific adaptation risk values from posterior inference. The developed risk learner can amortize expensive evaluation and provably approximately rank task difficulties in the pursuit of task robust adaptation. MPTS can be seamlessly integrated into zero-shot, few-shot, and many-shot learning paradigms. Extensive experimental results are conducted to exhibit the superiority of the proposed framework, remarkably increasing task adaptation robustness and retaining learning efficiency in contrast to existing state-of-the-art (SOTA) methods. The code is available at the project site https://github.com/thu-rllab/MPTS.

In this work, we initiate the systemic study of decision-theoretic metrics in the design and analysis of algorithms with machine-learned predictions. We introduce approaches based on both deterministic measures such as distance-based evaluation, that help us quantify how close the algorithm is to an ideal solution, as well as stochastic measures that allow us to balance the trade-off between the algorithm's performance and the risk associated with the imperfect oracle. These approaches help us quantify the algorithmic performance across the entire spectrum of prediction error, unlike several previous works that focus on few, and often extreme values of the error. We apply these techniques to two well-known problems from resource allocation and online decision making, namely contract scheduling and 1-max search.

In domains such as finance, healthcare, and robotics, managing worst-case scenarios is critical, as failure to do so can lead to catastrophic outcomes. Distributional Reinforcement Learning (DRL) provides a natural framework to incorporate risk sensitivity into decision-making processes. However, existing approaches face two key limitations: (1) the use of fixed risk measures at each decision step often results in overly conservative policies, and (2) the interpretation and theoretical properties of the learned policies remain unclear. While optimizing a static risk measure addresses these issues, its use in the DRL framework has been limited to the simple static CVaR risk measure. In this paper, we present a novel DRL algorithm with convergence guarantees that optimizes for a broader class of static Spectral Risk Measures (SRM). Additionally, we provide a clear interpretation of the learned policy by leveraging the distribution of returns in DRL and the decomposition of static coherent risk measures. Extensive experiments demonstrate that our model learns policies aligned with the SRM objective, and outperforms existing risk-neutral and risk-sensitive DRL models in various settings.

Offline reinforcement learning (RL) presents distinct challenges as it relies solely on observational data. A central concern in this context is ensuring the safety of the learned policy by quantifying uncertainties associated with various actions and environmental stochasticity. Traditional approaches primarily emphasize mitigating epistemic uncertainty by learning risk-averse policies, often overlooking environmental stochasticity. In this study, we propose an uncertainty-aware distributional offline RL method to simultaneously address both epistemic uncertainty and environmental stochasticity. We propose a model-free offline RL algorithm capable of learning risk-averse policies and characterizing the entire distribution of discounted cumulative rewards, as opposed to merely maximizing the expected value of accumulated discounted returns. Our method is rigorously evaluated through comprehensive experiments in both risk-sensitive and risk-neutral benchmarks, demonstrating its superior performance.

While reinforcement learning has shown experimental success in a number of applications, it is known to be sensitive to noise and perturbations in the parameters of the system, leading to high variance in the total reward amongst different episodes on slightly different environments. To introduce robustness, as well as sample efficiency, risk-sensitive reinforcement learning methods are being thoroughly studied. In this work, we provide a definition of robust reinforcement learning policies and formulate a risk-sensitive reinforcement learning problem to approximate them, by solving an optimization problem with respect to a modified objective based on exponential criteria. In particular, we study a model-free risksensitive variation of the widely-used Monte Carlo Policy Gradient algorithm, and introduce a novel risk-sensitive online Actor-Critic algorithm based on solving a multiplicative Bellman equation using stochastic approximation updates. Analytical results suggest that the use of exponential criteria generalizes commonly used ad-hoc regularization approaches, improves sample efficiency, and introduces robustness with respect to perturbations in the model parameters and the environment. The implementation, performance, and robustness properties of the proposed methods are evaluated in simulated experiments.

Offline reinforcement learning (RL) is suitable for safety-critical domains where online exploration is too costly or dangerous. In such safety-critical settings, decision-making should take into consideration the risk of catastrophic outcomes. In other words, decision-making should be risk-sensitive. Previous works on risk in offline RL combine together offline RL techniques, to avoid distributional shift, with risk-sensitive RL algorithms, to achieve risk-sensitivity. In this work, we propose risk-sensitivity as a mechanism to jointly address both of these issues. Our model-based approach is risk-averse to both epistemic and aleatoric uncertainty. Risk-aversion to epistemic uncertainty prevents distributional shift, as areas not covered by the dataset have high epistemic uncertainty. Risk-aversion to aleatoric uncertainty discourages actions that may result in poor outcomes due to environment stochasticity. Our experiments show that our algorithm achieves competitive performance on deterministic benchmarks, and outperforms existing approaches for risk-sensitive objectives in stochastic domains.

The process of designing costmaps for off-road driving tasks is often a challenging and engineering-intensive task. Recent work in costmap design for off-road driving focuses on training deep neural networks to predict costmaps from sensory observations using corpora of expert driving data. However, such approaches are generally subject to over-confident mispredictions and are rarely evaluated in-the-loop on physical hardware. We present an inverse reinforcement learning-based method of efficiently training deep cost functions that are uncertainty-aware. We do so by leveraging recent advances in highly parallel model-predictive control and robotic risk estimation. In addition to demonstrating improvement at reproducing expert trajectories, we also evaluate the efficacy of these methods in challenging off-road navigation scenarios. We observe that our method significantly outperforms a geometric baseline, resulting in 44% improvement in expert path reconstruction and 57% fewer interventions in practice. We also observe that varying the risk tolerance of the vehicle results in qualitatively different navigation behaviors, especially with respect to higher-risk scenarios such as slopes and tall grass.

Planning in Markov decision processes (MDPs) typically optimises the expected cost. However, optimising the expectation does not consider the risk that for any given run of the MDP, the total cost received may be unacceptably high. An alternative approach is to find a policy which optimises a risk-averse objective such as conditional value at risk (CVaR). In this work, we begin by showing that there can be multiple policies which obtain the optimal CVaR. We formulate the lexicographic optimisation problem of minimising the expected cost subject to the constraint that the CVaR of the total cost is optimal. We present an algorithm for this problem and evaluate our approach on three domains, including a road navigation domain based on real traffic data. Our experimental results demonstrate that our lexicographic approach attains improved expected cost while maintaining the optimal CVaR.

A large class of decision making under uncertainty problems can be described via Markov decision processes (MDPs) or partially observable MDPs (POMDPs), with application to artificial intelligence and operations research, among others. Traditionally, policy synthesis techniques are proposed such that a total expected cost or reward is minimized or maximized. However, optimality in the total expected cost sense is only reasonable if system behavior in the large number of runs is of interest, which has limited the use of such policies in practical mission-critical scenarios, wherein large deviations from the expected behavior may lead to mission failure. In this paper, we consider the problem of designing policies for MDPs and POMDPs with objectives and constraints in terms of dynamic coherent risk measures, which we refer to as the constrained risk-averse problem. For MDPs, we reformulate the problem into a infsup problem via the Lagrangian framework and propose an optimization-based method to synthesize Markovian policies. For MDPs, we demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. For POMDPs, we show that, if the coherent risk measures can be defined as a Markov risk transition mapping, an infinite-dimensional optimization can be used to design Markovian belief-based policies. For stochastic finite-state controllers (FSCs), we show that the latter optimization simplifies to a (finite-dimensional) DCP and can be solved by the DCCP framework. We incorporate these DCPs in a policy iteration algorithm to design risk-averse FSCs for POMDPs.