Research

Growing in the Wild: Equipping Robots with a Bayesian Brain

As autonomous vehicles, robotic platforms, and networks of edge devices become increasingly ubiquitous, robotic systems must step out of controlled laboratory settings and into the wild—into unstructured, uncertain, and unstable real-world scenarios. However, real-world deployment brings a profound shift in challenge: feedback is sparse and expensive, environments become unpredictable, and conditions change without warning. Current AI approaches, which rely heavily on static, offline training with large, labeled datasets, struggle under these constraints. To thrive in the wild, robots must learn from limited data, act under uncertainty, and adapt in real time.

This desideratum leads me to a fundamental inquiry, which also serves as the driving force behind my research:

How to build robots that can grow in the wild—capable of self-evolving in unstructured, uncertain, and unstable real-world scenarios?

I believe the answer lies in reverse-engineering the very principles behind human reasoning—Bayesian principles. Unlike today’s large foundation models, human cognition operates under a continual loop of belief updating and decision-making. We are natural Bayesians: we integrate new evidence with prior knowledge and choose actions that serve our goals in the face of uncertainty.

Drawing inspiration from the Bayesian brain hypothesis, I have distilled this cycle into four interlinked reasoning processes:

  1. Inference. In the wild, sensor feedback is both sparse and heterogeneous. To learn efficiently from limited data, robots must integrate information from distributed and different sensory modalities to yield a coherent percept.
  2. Inference-for-Decision. Processing information incurs computational cost and latency. To respond promptly under resource constraints, robots must strategically allocate their reasoning efforts.
  3. Decision. Real‑time decision‑making inevitably sacrifices model fidelity. And what makes things worse is the unavoidable noise. Ensuring robots act reliably under uncertainty thus becomes crucial when deploying them in the wild.
  4. Decision-for-Inference. Excessive caution can impede the very exploration needed to refine the imperfect models. Rather than passively awaiting data, robots should take proactive steps to acquire information.

Together, those four reasoning steps form a closed loop of Bayesian reasoning. Distinct from traditional approaches that often decouple learning from acting, this Bayesian‑loop embraces the perpetual dialogue between belief and action. It grants robots to perform efficient, prudent, and adaptive behaviors, which facilitates responsive, reliable, and resilient performance essential for real‑world deployment. My research program, therefore, can be summarized as “4R for 4R”:

Reverse-engineering 4 continual Reasoning processes underlying Bayesian brain to create Responsive, Reliable, and Resilient Robots.

Inference: Many Eyes, One Vision

In unstructured, uncertain environments, robots must construct meaningful interpretations of the world from limited, noisy, and often asynchronous data. Unlike in controlled lab settings, real-world deployment offers no guarantee of abundant, clean, or labeled observations. The challenge of online learning from limited data is thus foundational to autonomy.

Just as the human nervous system integrates signals from diverse modalities (e.g., vision, sound, touch…) into a unified percept, modern robotic systems increasingly rely on heterogeneous multi-agent teams where each robot has its unique sensing capabilities, perspectives, and roles. However, current classical data fusion methods usually assume synchronous data streams and full network connectivity, which is rarely satisfied in dynamic real-world scenarios.

To address this gap, I proposed a uniformly consistent distributed data fusion algorithm. This approach enables agents to harmonize partial, noisy observations into a shared probabilistic representation, even when network connections are sparse or intermittent.

Inference-for-Decision: Optimize Across Scales

Perception grants understanding, but action demands intention. To function in the wild, robots must go beyond recognizing their environment—they must make timely decisions under limited information and energy. This requires more than just choosing what to do—it demands choosing how much to think before doing: balancing the cost of reasoning with the benefit of better decisions.

Humans naturally navigate this tradeoff. When planning a cross-country trip, we sketch long-horizon goals (e.g., Boston to LA) while delaying detailed decisions (e.g., flight, rental, route) until closer in time, which allows us to conserve cognitive energy while remaining flexible to changing conditions. This principle—defer when uncertain, decide when informed—is deeply Bayesian. It reflects a compromise between model fidelity (having a fully accurate, precise plan) and resource efficiency (not exhausting energy or computation on what may soon become irrelevant).

To bring this principle into robotics, I developed an integrated task-and-motion planning framework built on a bi-level hierarchical architecture. The upper layer plans high-level symbolic actions, while the lower layer resolves detailed motion-level trajectories and constraints. Rather than fully simulating every motion path, the upper layer uses informed approximations to reason about what is feasible, deferring expensive refinements until truly needed.

Decision: Stay Alert to Risk

Strategic reasoning “frees” our computational burden, but the price we pay for “freedom” is the model fidelity. Let alone the fact that the model itself has its boundary: precise models can only emerge gradually from incrementally available data collected on the fly. This means that robots must take actions under imperfect models, and often in high-stakes situations.

Humans confront the same dilemma. When walking on uneven terrain, rather than waiting for full certainty, we act with caution by modulating force, trajectory, or timing to hedge against potential failures. This biological strategy highlights how we implicitly plan under model uncertainty by avoiding overconfident commitment before the environment is predictable.

Inspired by this, I developed a risk-averse model predictive control framework. Instead of relying on a single estimated model, the controller reasons over a distribution of candidate models, selecting actions that minimize expected regret rather than optimize mean performance. This approach explicitly treats model uncertainty as a design constraint, allowing the robot to act cautiously even amid ambiguity.

Decision-for-Inference: Curiosity is Knowledge

Excessive caution can paralyze learning, especially when precise models can only emerge through interaction. In this sense, curiosity becomes essential—not as a luxury, but as a mechanism for learning what cannot be pre-specified. Robots must not only respond to the world but seek to understand it, embodying a deeper principle: knowledge is not passive—it is earned through action.

This echoes the philosophy of Wang Yangming: “Knowledge is the beginning of action; action is the completion of knowledge.” This view aligns with active inference, a biologically inspired framework from computational neuroscience, which formalizes the idea of gathering information under the constraint that preferred outcomes are preserved. It sees intelligent behavior as a balance between curiosity and goal-seeking: to explore in ways that do not compromise core values.

Inspired by this, I developed a “regret-bounded exploration” paradigm that unifies Bayesian optimization and experimental design. Unlike traditional active learning approaches, this framework explicitly balances exploration and exploitation, ensuring that robots gather relevant information without drifting from desired behaviors.

  • Yingke Li, Anjali Parashar, Enlu Zhou and Chuchu Fan, “Unifying Bayesian Optimization and Experimental Design via Active Inference,” preprint.
  • Anjali Parashar, Joseph Zhang, Yingke Li and Chuchu Fan, “Cost-aware Discovery of Contextual Failures using Bayesian Active Learning,” 2025 Conference on Robot Learning (CoRL), accepted.

Potential Applications in the Wild

Those four reasoning steps close the complete loop of Bayesian reasoning that integrates belief updating, risk assessment, and curiosity-driven exploration into a unified, principled loop. This enables robots not only to act cautiously when uncertain, but also to seek information proactively to reduce ambiguity, ensuring performance does not stall in unfamiliar or data-scarce environments. Such capabilities are critical for real-world deployment. In space exploration, where data is sparse and communication is delayed, robots must autonomously refine models and make reliable decisions in the unknown. In underwater source seeking, where visibility is limited and dynamics are nonlinear, they must infer goals and adapt behavior on the fly. In search and rescue operations, robots must rapidly explore uncertain environments while accounting for safety and dynamically changing goals. Across these scenarios, the Bayesian closed-loop approach enables responsive, reliable, and resilient robots, empowering intelligent systems to operate where conventional methods fall short.

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