This paper develops a path planner that minimizes risk (e.g. motion execution) while maximizing accumulated reward (e.g., quality of sensor viewpoint) motivated by visual assistance or tracking scenarios in unstructured or confined environments. In these scenarios, the robot should maintain the best viewpoint as it moves to the goal. However, in unstructured or confined environments, some paths may increase the risk of collision; therefore there is a tradeoff between risk and reward. Conventional state-dependent risk or probabilistic uncertainty modeling do not consider path-level risk or is difficult to acquire. This risk-reward planner explicitly represents risk as a function of motion plans, i.e., paths. Without manual assignment of the negative impact to the planner caused by risk, this planner takes in a pre-established viewpoint quality map and plans target location and path leading to it simultaneously, in order to maximize overall reward along the entire path while minimizing risk. Exact and approximate algorithms are presented, whose solution is further demonstrated on a physical tethered aerial vehicle. Other than the visual assistance problem, the proposed framework also provides a new planning paradigm to address minimum-risk planning under dynamical risk and absence of substructure optimality and to balance the trade-off between reward and risk.
All existing methods require an artificial assignment of the adverse impact caused by risk, in the form of negative reward (penalty), unit cost, or bound on probability. Such assignment is not clear and a desired value may not even exist @cite_11 . It is subjective to human bias and hard to determine, e.g., how to define the value of better situational awareness compared to the cost of losing the robot. This paper avoids the necessity of such artificial assignment, e.g., manually arbitrating the value of either maximum acceptable risk or minimum expected reward. A utility function of the ratio between reward and risk along the entire path is proposed, as a measurement of how much risk is taken to achieve one unit of reward. In addition, the desirable goal state is not specified to the planner beforehand, but discovered by the planner based on optimal utility during the planning process.
@cite_11
2110790702
When controlling dynamic systems, such as mobile robots in uncertain environments, there is a trade off between risk and reward. For example, a race car can turn a corner faster by taking a more challenging path. This paper proposes a new approach to planning a control sequence with a guaranteed risk bound. Given a stochastic dynamic model, the problem is to find a control sequence that optimizes a performance metric, while satisfying chance constraints i.e. constraints on the upper bound of the probability of failure. We propose a two-stage optimization approach, with the upper stage optimizing the risk allocation and the lower stage calculating the optimal control sequence that maximizes reward. In general, the upper-stage is a non-convex optimization problem, which is hard to solve. We develop a new iterative algorithm for this stage that efficiently computes the risk allocation with a small penalty to optimality. The algorithm is implemented and tested on the autonomous underwater vehicle (AUV) depth planning problem, and demonstrates a substantial improvement in computation cost and suboptimality, compared to the prior arts. We study how to find plans that maximize the expected total utility for a given MDP, a planning objective that is important for decision making in high-stakes domains. The optimal actions can now depend on the total reward that has been accumulated so far in addition to the current state. We extend our previous work on functional value iteration from one-switch utility functions to all utility functions that can be approximated with piecewise linear utility functions (with and without exponential tails) by using functional value iteration to find a plan that maximizes the expected total utility for the approximate utility function. Functional value iteration does not maintain a value for every state but a value function that maps the total reward that has been accumulated so far into a value. We describe how functional value iteration represents these value functions in finite form, how it performs dynamic programming by manipulating these representations and what kinds of approximation guarantees it is able to make. We also apply it to a probabilistic blocksworld problem, a standard test domain for decision-theoretic planners. The expected return is a widely used objective in decision making under uncertainty. Many algorithms, such as value iteration, have been proposed to optimize it. In risk-aware settings, however, the expected return is often not an appropriate objective to optimize. We propose a new optimization objective for risk-aware planning and show that it has desirable theoretical properties. We also draw connections to previously proposed objectives for risk-aware planing: minmax, exponential utility, percentile and mean minus variance. Our method applies to an extended class of Markov decision processes: we allow costs to be stochastic as long as they are bounded. Additionally, we present an efficient algorithm for optimizing the proposed objective. Synthetic and real-world experiments illustrate the effectiveness of our method, at scale. Rewards are crucial objects that induce learning, approach behavior, choices, and emotions. Whereas emotions are difficult to investigate in animals, the learning function is mediated by neuronal reward prediction error signals which implement basic constructs of reinforcement learning theory. These signals are found in dopamine neurons, which emit a global reward signal to striatum and frontal cortex, and in specific neurons in striatum, amygdala, and frontal cortex projecting to select neuronal populations. The approach and choice functions involve subjective value, which is objectively assessed by behavioral choices eliciting internal, subjective reward preferences. Utility is the formal mathematical characterization of subjective value and a prime decision variable in economic choice theory. It is coded as utility prediction error by phasic dopamine responses. Utility can incorporate various influences, including risk, delay, effort, and social interaction. Appropriate for formal decision mechanisms, rewards are coded as object value, action value, difference value, and chosen value by specific neurons. Although all reward, reinforcement, and decision variables are theoretical constructs, their neuronal signals constitute measurable physical implementations and as such confirm the validity of these concepts. The neuronal reward signals provide guidance for behavior while constraining the free will to act. We provide a method, based on the theory of Markov decision processes, for efficient planning in stochastic domains. Goals are encoded as reward functions, expressing the desirability of each world state; the planner must find a policy (mapping from states to actions) that maximizes future rewards. Standard goals of achievement, as well as goals of maintenance and prioritized combinations of goals, can be specified in this way. An optimal policy can be found using existing methods, but these methods require time at best polynomial in the number of states in the domain, where the number of states is exponential in the number of propositions (or state variables). By using information about the starting state, the reward function, and the transition probabilities of the domain, we restrict the planner''s attention to a set of world states that are likely to be encountered in satisfying the goal. Using this restricted set of states, the planner can generate more or less complete plans depending on the time it has available. Our approach employs several iterative refinement routines for solving different aspects of the decision making problem. We describe the meta-level control problem of deliberation scheduling , allocating computational resources to these routines. We provide different models corresponding to optimization problems that capture the different circumstances and computational strategies for decision making under time constraints. We consider precursor models in which all decision making is performed prior to execution and recurrent models in which decision making is performed in parallel with execution, accounting for the states observed during execution and anticipating future states. We describe experimental results for both the precursor and recurrent problems that demonstrate planning times that grow slowly as a function of domain size. Recent advances in Autonomous Underwater Vehicle (AUV) technology have facilitated the collection of oceanographic data at a fraction of the cost of ship-based sampling methods. Unlike oceanographic data collection in the deep ocean, operation of AUVs in coastal regions exposes them to the risk of collision with ships and land. Such concerns are particularly prominent for slow-moving AUVs since ocean current magnitudes are often strong enough to alter the planned path significantly. Prior work using predictive ocean currents relies upon deterministic outcomes, which do not account for the uncertainty in the ocean current predictions themselves. To improve the safety and reliability of AUV operation in coastal regions, we introduce two stochastic planners: (a) a Minimum Expected Risk planner and (b) a risk-aware Markov Decision Process, both of which have the ability to utilize ocean current predictions probabilistically. We report results from extensive simulation studies in realistic ocean current fields obtained from widely used regional ocean models. Our simulations show that the proposed planners have lower collision risk than state-of-the-art methods. We present additional results from field experiments where ocean current predictions were used to plan the paths of two Slocum gliders. Field trials indicate the practical usefulness of our techniques over long-term deployments, showing them to be ideal for AUV operations. In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in rewards in addition to maximizing a standard criterion. Variance-related risk measures are among the most common risk-sensitive criteria in finance and operations research. However, optimizing many such criteria is known to be a hard problem. In this paper, we consider both discounted and average reward Markov decision processes. For each formulation, we first define a measure of variability for a policy, which in turn gives us a set of risk-sensitive criteria to optimize. For each of these criteria, we derive a formula for computing its gradient. We then devise actor-critic algorithms for estimating the gradient and updating the policy parameters in the ascent direction. We establish the convergence of our algorithms to locally risk-sensitive optimal policies. Finally, we demonstrate the usefulness of our algorithms in a traffic signal control application. We study all-pay contests under incomplete information where the reward is a function of the contestant's type and effort. We analyse the optimal reward for the designer when the reward is either multiplicatively separable or additively separable in effort and type. In the multiplicatively separable environment the optimal reward is always positive while in the additively separable environment it may also be negative. In both environments, depending on the designer's utility, the optimal reward may either increase or decrease in the contestants' effort. Finally, in both environments, the designer's payoff depends only upon the expected value of the effort-dependent rewards and not the number of rewards. In this paper, we propose a new autonomous braking system based on deep reinforcement learning. The proposed autonomous braking system automatically decides whether to apply the brake at each time step when confronting the risk of collision using the information on the obstacle obtained by the sensors. The problem of designing brake control is formulated as searching for the optimal policy in Markov decision process (MDP) model where the state is given by the relative position of the obstacle and the vehicle's speed, and the action space is defined as whether brake is stepped or not. The policy used for brake control is learned through computer simulations using the deep reinforcement learning method called deep Q-network (DQN). In order to derive desirable braking policy, we propose the reward function which balances the damage imposed to the obstacle in case of accident and the reward achieved when the vehicle runs out of risk as soon as possible. DQN is trained for the scenario where a vehicle is encountered with a pedestrian crossing the urban road. Experiments show that the control agent exhibits desirable control behavior and avoids collision without any mistake in various uncertain environments. This thesis investigates risk-sensitive sequential decision-making problems in an uncertain environment. We rst introduce the axiomatic concept of valuation functions that generalize known concepts of risk measures in mathematical nance to cover most of the existing risk related models in various elds, in particular, behavioral economics and cognitive neuroscience. By applying this concept to Markov processes, we construct valuation maps and develop thereby a uni ed framework for incorporating risk into Markov decision processes on general spaces. Within the framework, we study mainly two types of in nite-horizon risk-sensitive criteria, discounted and average valuations, and solve the associated optimization problems by value iteration. For the discounted case, we propose a new discount scheme, which is di erent from the conventional form but consistent with existing literature, while for the average criterion, we state Lyapunov-type stability conditions that generalize known conditions for Markov chains to ensure the existence of solutions to the optimality equation and a geometric convergence rate for the value iteration. Applying a set of valuation functions, called utility-based shortfall, we derive a family of model-free risk-sensitive reinforcement learning algorithms for solving the optimization problems corresponding to risk-sensitive valuations. In addition, we nd that when appropriate utility functions are chosen, agents’ behaviors express key features of human behavior as predicted by prospect theory, for example, di erent risk preferences for gains and losses, as well as the shape of subjective probability curves. As a proof of principle for the applicability of the new algorithms, we apply them to two tasks, 1) to quantify human behavior in a sequential investment task and 2) to perform risk control in simulated algorithmic trading of stocks. In the rst task, the risk-sensitive variant provides a signi cantly better t to the behavioral data and it leads to an interpretation of the subject’s responses which is indeed consistent with prospect theory. The analysis of simultaneously measured fMRI signals show a signi cant correlation of the risk-sensitive temporal di erence error with BOLD signal change in the ventral striatum. In the second task, our algorithm outperforms the risk-neutral reinforcement learning algorithm by keeping the trading cost at a substantially low level at the spot when the 2010 Flash Crash happened, and signi cantly reducing the risk over the whole test period. This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low prob- abilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling. EXPECTED UTILITY THEORY has dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice (24), and widely applied as a descriptive model of economic behavior, e.g. (15, 4). Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory (47, 36), and that most people actually do, most of the time. The present paper describes several classes of choice problems in which preferences systematically violate the axioms of expected utility theory. In the light of these observations we argue that utility theory, as it is commonly interpreted and applied, is not an adequate descriptive model and we propose an alternative account of choice under risk. 2. CRITIQUE In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in rewards in addition to maximizing a standard criterion. Variance related risk measures are among the most common risk-sensitive criteria in finance and operations research. However, optimizing many such criteria is known to be a hard problem. In this paper, we consider both discounted and average reward Markov decision processes. For each formulation, we first define a measure of variability for a policy, which in turn gives us a set of risk-sensitive criteria to optimize. For each of these criteria, we derive a formula for computing its gradient. We then devise actor-critic algorithms that operate on three timescales--a TD critic on the fastest timescale, a policy gradient (actor) on the intermediate timescale, and a dual ascent for Lagrange multipliers on the slowest timescale. In the discounted setting, we point out the difficulty in estimating the gradient of the variance of the return and incorporate simultaneous perturbation approaches to alleviate this. The average setting, on the other hand, allows for an actor update using compatible features to estimate the gradient of the variance. We establish the convergence of our algorithms to locally risk-sensitive optimal policies. Finally, we demonstrate the usefulness of our algorithms in a traffic signal control application. Decision-theoretic planning with nonlinear utility functions is important since decision makers are often risk-sensitive in high-stake planning situations. One-switch utility functions are an important class of nonlinear utility functions that can model decision makers whose decisions change with their wealth level. We study how to maximize the expected utility of a Markov decision problem for a given one-switch utility function, which is difficult since the resulting planning problem is not decomposable. We first study an approach that augments the states of the Markov decision problem with the wealth level. The properties of the resulting infinite Markov decision problem then allow us to generalize the standard risk-neutral version of value iteration from manipulating values to manipulating functions that map wealth levels to values. We use a probabilistic blocks-world example to demonstrate that the resulting risk-sensitive version of value iteration is practical. Variance-penalized Markov decision processes (MDPs) for an infinite time horizon have been studied in the literature for asymptotic and one-step variance; in these models, the objective function is generally the expected long-run reward minus a constant times the variance, where variance is used as a measure of risk. For the finite time horizon, asymptotic variance has been considered in Collins [1], but this model accounts for only a terminal reward, i.e., reward is earned at the end of the time horizon. In this paper, we seek to develop a framework for one-step variance in the finite time horizon in which rewards can be non-zero in every state. We develop a solution algorithm based on the stochastic shortest path algorithm of Bertsekas and Tsitsiklis [2]. We also present a Q-Learning algorithm for a simulation-based scenario which applies in the absence of the transition probability model, along with some preliminary convergence results. Movement of materials, plant and site operative from one place to another on construction sites and construction workplaces are of paramount importance to site planners as savings in travel distance can reduce cost and increase productivity. In addition, risks on construction sites can be reduced if the use of vehicles and mobile plant is properly managed by setting out paths avoiding high risks areas. The work reported in this paper presents a framework for supporting path planning analysis of construction sites based on multi-objective evaluation of transport cost, safety, and visibility. This paper investigates the use of fuzzy-based multi-objective optimisation approach in making a more informed strategic decisions regarding the movement path of people and vehicles on construction sites, and detailed decisions regarding travel distance and operational paths on workplaces, enabling site planners to examine paths scenarios that are subjected to a high degree of uncertainty and subjectivity. The authors develop a theory characterizing optimal stopping times for discrete-time ergodic Markov processes with discounted rewards. The theory differs from prior work by its view of per-stage and terminal reward functions as elements of a certain Hilbert space. In addition to a streamlined analysis establishing existence and uniqueness of a solution to Bellman's equation, this approach provides an elegant framework for the study of approximate solutions. In particular, the authors propose a stochastic approximation algorithm that tunes weights of a linear combination of basis functions in order to approximate a value function. They prove that this algorithm converges (almost surely) and that the limit of convergence has some desirable properties. The utility of the approximation method is illustrated via a computational case study involving the pricing of a path dependent financial derivative security that gives rise to an optimal stopping problem with a 100-dimensional state space. Uncertainty complicates early requirements and architecture decisions and may expose a software project to significant risk. Yet software architects lack support for evaluating uncertainty, its impact on risk, and the value of reducing uncertainty before making critical decisions. We propose to apply decision analysis and multi-objective optimisation techniques to provide such support. We present a systematic method allowing software architects to describe uncertainty about the impact of alternatives on stakeholders' goals; to calculate the consequences of uncertainty through Monte-Carlo simulation; to shortlist candidate architectures based on expected costs, benefits and risks; and to assess the value of obtaining additional information before deciding. We demonstrate our method on the design of a system for coordinating emergency response teams. Our approach highlights the need for requirements engineering and software cost estimation methods to disclose uncertainty instead of hiding it. Recent work has advanced our knowledge of phasic dopamine reward prediction error signals. The error signal is bidirectional, reflects well the higher order prediction error described by temporal difference learning models, is compatible with model-free and model-based reinforcement learning, reports the subjective rather than physical reward value during temporal discounting and reflects subjective stimulus perception rather than physical stimulus aspects. Dopamine activations are primarily driven by reward, and to some extent risk, whereas punishment and salience have only limited activating effects when appropriate controls are respected. The signal is homogeneous in terms of time course but heterogeneous in many other aspects. It is essential for synaptic plasticity and a range of behavioural learning situations. We consider the design and analysis of algorithms that learn from the consequences of their actions with the goal of maximizing their cumulative reward, when the consequence of a given action is felt immediately, and a linear function, which is unknown a priori, (approximately) relates a feature vector for each action state pair to the (expected) associated reward. We focus on two cases, one in which a continuous-valued reward is (approximately) given by applying the unknown linear function, and another in which the probability of receiving the larger of binary-valued rewards is obtained. For these cases we provide bounds on the per-trial regret for our algorithms that go to zero as the number of trials approaches infinity. We also provide lower bounds that show that the rate of convergence is nearly optimal. Manipulation in clutter requires solving complex sequential decision making problems in an environment rich with physical interactions. The transfer of motion planning solutions from simulation to the real world, in open-loop, suffers from the inherent uncertainty in modelling real world physics. We propose interleaving planning and execution in real-time, in a closed-loop setting, using a Receding Horizon Planner (RHP) for pushing manipulation in clutter. In this context, we address the problem of finding a suitable value function based heuristic for efficient planning, and for estimating the cost-to-go from the horizon to the goal. We estimate such a value function first by using plans generated by an existing sampling-based planner. Then, we further optimize the value function through reinforcement learning. We evaluate our approach and compare it to state-of-the-art planning techniques for manipulation in clutter. We conduct experiments in simulation with artificially injected uncertainty on the physics parameters, as well as in real world tasks of manipulation in clutter. We show that this approach enables the robot to react to the uncertain dynamics of the real world effectively.