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When Information is Worth the Risk: Behavioral Valuation for Hazardous Robotic Exploration
Alkesh K. Srivastava, Aamodh Suresh, Carlos Nieto-Granda, Philip Dames
TL;DR
Hazardous exploration must balance uncertainty reduction against the possibility that sensing causes failure and eliminates future observations. This paper isolates that decision in a valuation layer, introducing Prelec-weighted Behavioral Information objectives while keeping inference, sensing, physical risk, and planning fixed. Theory and large-scale failure-truncated experiments show that valuation reshapes the information-risk frontier, with risk-aware objectives offering conservative and intermediate operating regimes alongside Shannon’s high-information baseline.
Problem
Hazardous exploration requires deciding when information reduction is worth the failure risk that can terminate execution and prevent future observations.
Method
The paper fixes Bayesian updates, sensing, physical risk, feasible paths, and finite-horizon planning, then changes only the path-ranking objective using risk-augmented Behavioral Information with Prelec weighting.
Results
Valuation alone reshapes the information-risk frontier: Shannon occupies the high-information/high-risk region, linear risk penalties reduce exposure, and Behavioral valuation adds nonlinear intermediate and conservative regimes.
Takeaways & Limitations
Robots can treat information-risk tradeoffs as an interpretable valuation choice rather than changing their underlying inference, sensing, or physical risk models.
Takeaways & Limitations
Linear scalarization may miss unsupported Pareto points in nonconvex tradeoff sets, and the Behavioral Information objective is a planning valuation functional rather than a replacement for Shannon mutual information.
Abstract
from arXiv · showhide
Hazardous robotic exploration requires robots to map spatial risks, such as unsafe terrain, radiation, fire, mines, or structural damage, while operating where collecting information can itself cause failure. A highly informative path may expose the robot to hazards, terminate execution, and prevent future observations. Hazardous exploration therefore requires deciding not only where uncertainty is largest, but when reducing it is worth the risk. This paper introduces a valuation-layer view of this problem. We keep the belief update, sensor model, physical risk model, and finite-horizon informative planner fixed, and change only the scalar objective used to rank feasible paths. Within this framework, we introduce a risk-augmented Behavioral Information objective based on Prelec probability weighting, yielding an interpretable family of conservative-to-aggressive information-risk valuations. Theoretically, we show that valuation parameters create switching boundaries between high-information/high-risk and lower-information/lower-risk paths, and induce a transformed Pareto-frontier structure over feasible exploration policies. Large-scale failure-truncated grid-world experiments show that valuation alone reshapes the information-risk frontier. Shannon information planning remains a strong raw-information baseline, while risk-aware objectives can reduce hazard exposure and robot losses by avoiding failures that truncate future sensing. Risk-augmented Behavioral valuation is Pareto-competitive with standard risk-aware baselines and provides interpretable conservative and intermediate regimes. These results support a framework in which robots reason not only about how much uncertainty an action reduces, but whether that reduction is worth the risk required to obtain it.
1 Introduction
Hazardous exploration couples information gathering with failure risk, so path selection must value whether uncertainty reduction justifies possible mission termination. The paper isolates this valuation layer and studies how alternative objectives reshape the same feasible information-risk tradeoff.
- Motivation: Hazardous exploration requires mapping risks while avoiding regions whose observation may destroy the robot and truncate future sensing.The most informative path can also be the most dangerous, coupling information value to survival.
- Valuation-layer view: The paper holds belief updates, sensing, physical risk, candidate paths, and planning fixed while changing only path valuation.This isolates how information-risk scoring alone changes exploration behavior.
- Approach: A risk-augmented Behavioral Information objective applies Prelec probability weighting at the objective layer without changing Bayesian beliefs or physical risk probabilities.The resulting family provides nonlinear information-risk valuations.
- Theory and evaluation: The analysis derives path-switching boundaries and a transformed Pareto interpretation, while experiments test valuation effects under failure-truncated execution.Different objectives can rank the same candidate paths differently.
- Contribution: Large-scale experiments show that valuation alone exposes a nontrivial information-risk frontier.The contribution is framed as a valuation problem layered on standard Bayesian planning.
2 Related Work
Related work spans informative planning, failure-truncated sensing, risk-aware planning, behavioral probability weighting, and multiobjective decision making. This paper distinguishes itself by applying nonlinear probability weighting only to path valuation under otherwise fixed inference, sensing, risk, and planning components.
- Informative Path Planning and Active Sensing: Informative path planning selects actions that reduce uncertainty using objectives such as entropy reduction or mutual information.Prior work includes mobile-robot information gain, information-theoretic control, distributed sensing, active sensing, and risky cooperative search.
- Failure-Truncated and Path-Based Sensing: Failure-truncated sensing studies information gathering when execution can terminate observations, whereas this paper uses cell-level binary hazard observations along executed paths.The settings share failure-coupled information gathering but differ in sensing representation.
- Risk-Aware and Survivability-Constrained Planning: Risk-aware planning regulates hazards through constraints or penalties, including survivability constraints, expendable-team planning, and CVaR-based viewpoint selection.These methods primarily regulate risk directly rather than isolating valuation as a separate design layer.
- Behavioral Probability Weighting and Behavioral Entropy: Behavioral probability weighting and Behavioral Entropy motivate nonlinear uncertainty valuation, but prior work does not isolate the single-agent information-failure tradeoff under fixed planning components.The paper applies probability weighting only at valuation while leaving beliefs, sensing, and physical risks unchanged.
- Multiobjective Planning and the Valuation-Layer Gap: Multiobjective planning represents competing exploration tradeoffs, while this setting studies how a valuation functional ranks information-risk alternatives.The paper connects its objective to a transformed information-risk tradeoff set.
3 Hazardous Exploration as a Valuation Problem
The framework models a robot that infers a spatial hazard map while selecting finite-horizon paths that provide information but may cause failure. Candidate paths share one feasible set and differ only through the scalar valuation used to rank their information and physical risk.
- Model: The robot maintains Bayesian marginal beliefs over binary latent hazards and evaluates feasible finite-horizon candidate paths at each decision epoch.Beliefs represent estimated hazard locations, while paths are generated under robot dynamics and grid constraints.
- Candidate paths: All methods use the same feasible path set, differing only in how candidate paths are valued.This assumption enables comparisons that isolate the objective rather than feasibility or planning search.
- Sensing and belief update: Each visited cell yields a noisy binary hazard observation, after which the robot updates its hazard belief through a Bayesian operator.The observation model is characterized by true-positive and false-positive rates.
- Information and risk: Path information is measured as expected reduction in total Shannon hazard-belief entropy, while physical risk is represented through expected exposure and path failure probability.The experiments use expected hazard failure probability over unique visited cells as the hazard-risk term.
- Valuation problem: The central question is how the choice of scalar objective changes exploration when feasible paths, Bayesian updates, sensing, and physical risk remain fixed.This formulates hazardous exploration as a valuation problem layered on ordinary inference and finite-horizon planning.
4 Behavioral Risk Valuation
The paper defines a Behavioral valuation family that changes how information and risk are scored while preserving ordinary Bayesian inference and physical risk generation. Prelec curvature supplies conservative-to-aggressive risk valuation, and an explicit parameter trades Behavioral Information Gain against perceived failure risk.
- Valuation design: Probability weighting is applied only at the objective layer, changing how information and risk are valued before path selection.The belief update, sensor model, and physical risk probabilities remain unchanged.
- Prelec weighting: Prelec weighting uses α for curvature and β for its nontrivial fixed point; experiments fix β=1 to isolate curvature and risk sensitivity.The identity case α=1 gives w_α(p)=p.
- Risk curvature: For α<1, small probabilities are overweighted and rare hazards receive more conservative valuation, whereas α>1 can produce more aggressive valuation.This changes perceived risk without changing the underlying physical risk probability.
- Behavioral Entropy and Behavioral Information Gain: Behavioral Entropy applies Prelec-weighted probabilities to cell-wise Bernoulli hazard beliefs, and Behavioral Information Gain measures expected reduction in that entropy.Only the entropy functional changes; posterior beliefs and expectations remain ordinary Bayesian quantities.
- Interpretation: Behavioral Information Gain is a planning valuation functional rather than a replacement theorem for Shannon mutual information.This distinction follows because probability weighting changes the entropy functional.
- Risk-Augmented Behavioral Objective: The risk-augmented objective subtracts η times weighted expected hazard failure probability from Behavioral Information Gain, with η controlling explicit risk sensitivity.Prelec weighting affects candidate-path ranking before execution, not belief updates or sampled failures.
- Special cases: With α=1 the risk term is linear, and with η=0 and α=1 the normalized Behavioral Information Gain reduces to Shannon information gain in the binary-cell setting.These cases connect the proposed family to standard linear risk penalization and Shannon planning.
5 Theoretical Analysis
The analysis isolates valuation as the source of path-selection changes: fixed feasible paths and models are ranked by a risk-augmented Behavioral objective. Its parameters create switching boundaries and select supported points on a transformed information-risk frontier.
- Valuation changes path rankings while the Bayesian update, sensor and physical-risk models, feasible paths, and search procedure remain fixed.This makes the analysis a controlled study of the scalar objective rather than a comparison of planners or filters.
- 5.1 Valuation-Induced Path Switching: When a path is more informative but riskier, lower risk sensitivity favors it, whereas sufficiently high risk sensitivity favors the lower-risk alternative.The switching occurs at the boundary η*=ΔB_α/ΔW_α.
- 5.1 Valuation-Induced Path Switching: Changing α can move fixed candidate paths across preference regimes because probability weighting changes both Behavioral Information value and perceived risk.The resulting switching curve η*(α) is generally nonmonotone and lacks a closed-form solution.
- 5.2 Transformed Information-Risk Frontier: For fixed α, the objective linearly scalarizes perceived risk and Behavioral Information in transformed space, so unique maximizers are supported Pareto points.Changing η changes the supporting slope, while changing α changes the transformed frontier geometry.
- 5.2 Transformed Information-Risk Frontier: Varying η selects different supported frontier points, allowing conservative, intermediate, and aggressive regimes without modifying the Bayesian filter or planner.The feasible paths remain fixed; valuation changes their transformed coordinates and rankings.
- 5.2 Transformed Information-Risk Frontier: The scalarization does not recover unsupported Pareto points on nonconvex portions of the transformed tradeoff set.Useful intermediate information-risk policies may therefore require constrained or explicitly multiobjective methods.
6 Experimental Design
The experiments isolate valuation effects by holding the planning, sensing, belief-update, and physical-risk substrate fixed while evaluating failure-truncated exploration across two stages.
- Experimental setup: The shared planner evaluates candidate paths with common information and risk models, ranks them using the selected objective, executes the highest-valued path, and updates beliefs from collected observations.Failure truncation stops execution after hazard- or malfunction-induced failure, preventing later planned observations and restarting the next deployment from the base.
- Experimental stages: Stage 1 evaluates clustered and frontier-risk hazard structures, while Stage 2 tests a reduced objective set across additional structures, densities, and lethality values.The design includes 13,600 Stage 1 scenario–method–seed runs and 36,000 Stage 2 runs, with 40 deployments per run.
- Metrics: The evaluation reports entropy reduction, expected hazard and total risk, sampled losses, and Pareto nondominance, with losses separated into hazard- and malfunction-induced components.Entropy reduction is measured as summed Shannon hazard-belief entropy decrease in nats, without map-size normalization.
- Filtering: Near-zero exploration, near-base behavior, and frequent infeasible or no-op paths are marked degenerate, so analysis focuses on the filtered nondegenerate frontier.
7 Results
Changing only the valuation objective reshapes the information-risk frontier: Shannon favors high information and risk, while Behavioral valuation supplies interpretable intermediate and conservative regimes that remain competitive across scenarios.
- 7.1 Valuation Reshapes the Information-Risk Frontier: Risk-augmented Behavioral settings add nonlinear intermediate and conservative operating points to the Stage 1 information-risk frontier, while Shannon occupies the high-information/high-risk region.The frontier is produced under identical planning, sensing, Bayesian-update, and physical-risk models; risk-penalized Shannon remains a strong linear-risk baseline.
- 7.1 Valuation Reshapes the Information-Risk Frontier: Shannon planning collects 1/8 planned observations after early failure, whereas Behavioral valuation completes execution and collects 8/8 observations on the same representative rollout.
- 7.1 Valuation Reshapes the Information-Risk Frontier: Behavioral parameter sweeps organize policies into aggressive, intermediate, conservative, and suppressed-exploration regimes by varying perceived-risk weighting and risk-probability distortion.The paper recommends selecting (𝛼, 𝜂) according to mission-level risk tolerance rather than prescribing a universal pair.
- 7.1 Valuation Reshapes the Information-Risk Frontier: Failure truncation makes intermediate frontier points useful because high predicted information may not be realized after early failure, whereas excessive conservatism can suppress exploration.
- 7.2 Robustness: Across additional hazard structures, densities, and lethality values, several risk-augmented Behavioral settings repeatedly appear on the filtered nondegenerate frontier, alongside frequent risk-penalized Shannon performance.
8 Conclusion
The paper presents valuation as a distinct design layer for hazardous exploration, isolating how path-ranking objectives determine when information is worth the risk of failure and lost future sensing.
- Conclusion: Holding belief updates, sensing, physical risk, feasible paths, and planning fixed while changing only path ranking isolates valuation as a separate layer for hazardous exploration.
- Conclusion: The risk-augmented Behavioral Information objective provides interpretable nonlinear information-risk tradeoffs for reasoning about when information acquisition is worth its operational risk.