Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions (2310.05921v3)

Abstract: We introduce Conformal Decision Theory, a framework for producing safe autonomous decisions despite imperfect machine learning predictions. Examples of such decisions are ubiquitous, from robot planning algorithms that rely on pedestrian predictions, to calibrating autonomous manufacturing to exhibit high throughput and low error, to the choice of trusting a nominal policy versus switching to a safe backup policy at run-time. The decisions produced by our algorithms are safe in the sense that they come with provable statistical guarantees of having low risk without any assumptions on the world model whatsoever; the observations need not be I.I.D. and can even be adversarial. The theory extends results from conformal prediction to calibrate decisions directly, without requiring the construction of prediction sets. Experiments demonstrate the utility of our approach in robot motion planning around humans, automated stock trading, and robot manufacturing.

• The paper introduces Conformal Decision Theory (CDT), which calibrates decision parameters on the fly to achieve statistically guaranteed low-risk decisions.
• It employs conformal controllers and a tunable parameter to dynamically balance safety and performance, providing finite-time risk bounds.
• Experimental validation in robot navigation, automated stock trading, and manufacturing confirms CDT’s practical effectiveness versus traditional prediction-set approaches.

Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions

The paper presents Conformal Decision Theory (CDT), an innovative framework addressing the challenge of making safe autonomous decisions under imperfect machine learning predictions. The crux of the theory is to calibrate decisions directly rather than relying solely on calibrated prediction sets. This paradigm shift is designed to ensure statistically guaranteed low-risk decisions without assumptions about the distribution or model of the underlying data, which can be adversarial.

Core Concepts and Contributions

The central idea of CDT is encapsulated in the concept of conformal controllers—an algorithmic approach to dynamically adjusting decision-making parameters to balance risk and performance. Specifically, these controllers utilize a conformal control variable, $\lambda_t$, which acts as a tunable parameter to influence the conservatism or aggressiveness of decisions over time. Through this mechanism, CDT delivers finite-time risk bounds for sequences of decisions, effectively controlling the empirical risk of these decisions within predefined thresholds. The paper extends the idea of conformal prediction to decision-making directly, bypassing the need for prediction-set-based approaches that may be excessively conservative and computationally intensive.

Among the contributions of this paper are:

1. Introduction of CDT, employing conformal controllers to achieve calibrated decision-making, extending existing methodologies in adaptive conformal prediction.
2. Provision of finite-time risk bounds, offering stronger results compared to existing techniques.
3. Demonstration of CDT's utility across three practical domains: robot navigation, automated stock trading, and robot manufacturing.

Practical Implications and Experimental Validation

The implications of Conformal Decision Theory are considerable, particularly for fields that prioritize decision quality over predictive accuracy. Domains like control theory, reinforcement learning, and logistics can reap benefits from this framework because it aligns risk control directly with decisions rather than predictions, which are often secondary in practical applications.

The paper illustrates CDT's effectiveness in three autonomous decision-making domains:

• Robot Navigation: CDT is employed to calibrate a robot's path planning, ensuring safety around pedestrians without compromising efficiency.
• Manufacturing Assembly: A factory conveyor belt system adjusts speed for optimal throughput while maintaining a low failure rate in robot grasps.
• Stock Trading: An autonomous agent controls trading action based on imperfect predictive models, adhering to loss thresholds.

The experimental results demonstrate that CDT consistently maintains risk within the desired boundaries while yielding competitive, if not superior, utility compared to traditional prediction-based approaches.

Future Developments

Looking forward, CDT opens several avenues for research and development:

1. Refinement of batch settings for conformal decision-making, particularly in scenarios where offline datasets or simulators support comprehensive decision evaluation.
2. Expansion of CDT into non-exchangeable settings and streamlining its computational practicality, especially in domains demanding near real-time decision-making.
3. Investigation into decision set optimizations where the tuning of multiple parameters may enhance utility while adhering to conformal risk bounds.

Conformal Decision Theory bridges prediction and decision-making, providing robust risk-bound guarantees while optimizing decision outputs, making it a valuable advancement for autonomous systems seeking reliability despite imperfect predictions.