10,574 research outputs found
Risk of Stochastic Systems for Temporal Logic Specifications
The wide availability of data coupled with the computational advances in
artificial intelligence and machine learning promise to enable many future
technologies such as autonomous driving. While there has been a variety of
successful demonstrations of these technologies, critical system failures have
repeatedly been reported. Even if rare, such system failures pose a serious
barrier to adoption without a rigorous risk assessment. This paper presents a
framework for the systematic and rigorous risk verification of systems. We
consider a wide range of system specifications formulated in signal temporal
logic (STL) and model the system as a stochastic process, permitting
discrete-time and continuous-time stochastic processes. We then define the STL
robustness risk as the risk of lacking robustness against failure. This
definition is motivated as system failures are often caused by missing
robustness to modeling errors, system disturbances, and distribution shifts in
the underlying data generating process. Within the definition, we permit
general classes of risk measures and focus on tail risk measures such as the
value-at-risk and the conditional value-at-risk. While the STL robustness risk
is in general hard to compute, we propose the approximate STL robustness risk
as a more tractable notion that upper bounds the STL robustness risk. We show
how the approximate STL robustness risk can accurately be estimated from system
trajectory data. For discrete-time stochastic processes, we show under which
conditions the approximate STL robustness risk can even be computed exactly. We
illustrate our verification algorithm in the autonomous driving simulator CARLA
and show how a least risky controller can be selected among four neural network
lane keeping controllers for five meaningful system specifications
Risk-Sensitive Path Planning via CVaR Barrier Functions: Application to Bipedal Locomotion
Enforcing safety of robotic systems in the presence of stochastic uncertainty is a challenging problem. Traditionally,researchers have proposed safety in the statistical mean as a safety measure in this case. However, ensuring safety in the statistical mean is only reasonable if robot safe behavior in the large number of runs is of interest, which precludes the use of mean safety in practical scenarios. In this paper, we propose a risk sensitive notion of safety called conditional-value-at-risk (CVaR) safety, which is concerned with safe performance in the worst case realizations. We introduce CVaR barrier functions asa tool to enforce CVaR safety and propose conditions for their Boolean compositions. Given a legacy controller, we show that we can design a minimally interfering CVaR safe controller via solving difference convex programs. We elucidate the proposed method by applying it to a bipedal locomotion case study
On Optimizing the Conditional Value-at-Risk of a Maximum Cost for Risk-Averse Safety Analysis
The popularity of Conditional Value-at-Risk (CVaR), a risk functional from
finance, has been growing in the control systems community due to its intuitive
interpretation and axiomatic foundation. We consider a non-standard optimal
control problem in which the goal is to minimize the CVaR of a maximum random
cost subject to a Borel-space Markov decision process. The objective takes the
form , where is a
risk-aversion parameter representing a fraction of worst cases, is a
stage or terminal cost, and is the length of a finite
discrete-time horizon. The objective represents the maximum departure from a
desired operating region averaged over a given fraction of worst
cases. This problem provides a safety criterion for a stochastic system that is
informed by both the probability and severity of the potential consequences of
the system's trajectory. In contrast, existing safety analysis frameworks apply
stage-wise risk constraints (i.e., must be small for all , where
is a risk functional) or assess the probability of constraint violation
without quantifying its possible severity. To the best of our knowledge, the
problem of interest has not been solved. To solve the problem, we propose and
study a family of stochastic dynamic programs on an augmented state space. We
prove that the optimal CVaR of a maximum cost enjoys an equivalent
representation in terms of the solutions to this family of dynamic programs
under appropriate assumptions. We show the existence of an optimal policy that
depends on the dynamics of an augmented state under a measurable selection
condition. Moreover, we demonstrate how our safety analysis framework is useful
for assessing the severity of combined sewer overflows under precipitation
uncertainty.Comment: A shorter version is under review for IEEE Transactions on Automatic
Control, submitted December 202
Distributional Probabilistic Model Checking
Probabilistic model checking can provide formal guarantees on the behavior of
stochastic models relating to a wide range of quantitative properties, such as
runtime, energy consumption or cost. But decision making is typically with
respect to the expected value of these quantities, which can mask important
aspects of the full probability distribution such as the possibility of
high-risk, low-probability events or multimodalities. We propose a
distributional extension of probabilistic model checking, applicable to
discrete-time Markov chains (DTMCs) and Markov decision processes (MDPs). We
formulate distributional queries, which can reason about a variety of
distributional measures, such as variance, value-at-risk or conditional
value-at-risk, for the accumulation of reward until a co-safe linear temporal
logic formula is satisfied. For DTMCs, we propose a method to compute the full
distribution to an arbitrary level of precision, based on a graph analysis and
forward analysis of the model. For MDPs, we approximate the optimal policy with
respect to expected value or conditional value-at-risk using distributional
value iteration. We implement our techniques and investigate their performance
and scalability across a range of benchmark models. Experimental results
demonstrate that our techniques can be successfully applied to check various
distributional properties of large probabilistic models.Comment: 20 pages, 2 pages appendix, 5 figures. Submitted for review. For
associated Github repository, see
https://github.com/davexparker/prism/tree/ing
Risk-Averse Planning Under Uncertainty
We consider the problem of designing policies for partially observable Markov decision processes (POMDPs) with dynamic coherent risk objectives. Synthesizing risk-averse optimal policies for POMDPs requires infinite memory and thus undecidable. To overcome this difficulty, we propose a method based on bounded policy iteration for designing stochastic but finite state (memory) controllers, which takes advantage of standard convex optimization methods. Given a memory budget and optimality criterion, the proposed method modifies the stochastic finite state controller leading to sub-optimal solutions with lower coherent risk
Generative Modeling of Residuals for Real-Time Risk-Sensitive Safety with Discrete-Time Control Barrier Functions
A key source of brittleness for robotic systems is the presence of model
uncertainty and external disturbances. Most existing approaches to robust
control either seek to bound the worst-case disturbance (which results in
conservative behavior), or to learn a deterministic dynamics model (which is
unable to capture uncertain dynamics or disturbances). This work proposes a
different approach: training a state-conditioned generative model to represent
the distribution of error residuals between the nominal dynamics and the actual
system. In particular we introduce the Online Risk-Informed Optimization
controller (ORIO), which uses Discrete-Time Control Barrier Functions, combined
with a learned, generative disturbance model, to ensure the safety of the
system up to some level of risk. We demonstrate our approach in both
simulations and hardware, and show our method can learn a disturbance model
that is accurate enough to enable risk-sensitive control of a quadrotor flying
aggressively with an unmodelled slung load. We use a conditional variational
autoencoder (CVAE) to learn a state-conditioned dynamics residual distribution,
and find that the resulting probabilistic safety controller, which can be run
at 100Hz on an embedded computer, exhibits less conservative behavior while
retaining theoretical safety properties.Comment: 9 pages, 6 figures, submitted to the 2024 IEEE International
Conference on Robotics and Automation (ICRA 2024
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