When Gradients Mislead: Why Adam Helps One Throttle Valve and Hurts Another

An optimizer meets sticky hardware

In Learning to Tune with Biased Gradients, Félix Martinez-Jiménez, Sander Miller-Murphy, Tobie Ondoa-Essomba and Emmanuel Witrant study a physical counterpart of a familiar AI problem: optimizing parameters using imperfect gradients. Their system is an automotive electronic throttle valve, where a motor works against a return spring and friction. Stiction—the resistance that keeps a stationary mechanism from moving—makes repeated experiments behave differently even when the valve starts at the same angle.

The work is an arXiv preprint posted on November 4, 2026. Its findings concern ten simulated valves and two hardware units, not a general verdict on adaptive optimization.

How experiments become gradients

The researchers use iterative feedback tuning, or IFT, to adjust a fixed controller without requiring a plant model. Each iteration runs two closed-loop experiments. The first measures how well the valve follows a target trajectory. The second feeds a scaled version of the first experiment's tracking error back into the system. Its response estimates how changes in controller parameters affect the output and control input.

The objective combines squared tracking error with a penalty on control-input deviations. The controller is called an intelligent proportional controller, but its implemented form is equivalent to an incremental proportional–integral controller. Optimization takes place in the logarithms of two positive parameters, K and alpha, keeping them positive and making updates relative rather than absolute.

IFT's gradient estimate is unbiased under linear-system assumptions with suitable noise conditions and matching initial states. The valves violate those assumptions. At the same resting angle, stiction permits different motor commands to hold equilibrium. Consequently, the controller's stored integral state can differ between the two experiments.

For a linear plant with a constant input offset representing this mismatch, the authors derive an extra gradient-error term proportional to the offset divided by the second experiment's amplitude. Making that experiment smaller can therefore amplify the error rather than improve the approximation. Making it much larger risks saturation and mechanical stops. The derivation isolates one mechanism; it does not fully describe repeated sticking during nonlinear motion.

Testing whether the direction is useful

The team fits digital twins of ten valves using recorded excitation and staircase experiments, including asymmetric friction, stiction and physical stops. They compare IFT estimates with central finite-difference gradients on a parameter grid.

In the lower-cost half of that grid, the estimated gradient points in a local descent direction only 69% of the time on average, ranging from 54% to 80% across twins. This is a fraction of sampled parameter settings, not a hardware success rate. Removing Coulomb friction and stiction raises the average to 93%; removing input saturation barely changes it, to 70%.

Across 40-iteration tuning runs, well-tuned update rules typically close about half the initial gap to a grid-based optimum within 10–15 iterations, then stall. Continuing can make things worse: 19–46% of runs finish above the initial cost, even without added noise. Adam reduces severe deterioration in some noisy simulations, but does not eliminate the underlying gradient problem.

Two valves, opposite outcomes

On hardware valve A, changing the experiment to cover the validation range and placing the second experiment away from the stops reduces the cost's coefficient of variation from 19% to 6.3%. Nevertheless, the K gradient component remains dominated by noise.

Adam's coordinate-wise normalization gives more movement to a useful direction that Gauss–Newton suppresses, while momentum helps extract a weak trend in the noisy coordinate. Separate endpoint validation measurements give root-mean-square tracking errors of 6.73 degrees for Adam and 6.82 degrees for Gauss–Newton, versus 7.26 degrees initially. That advantage has a tradeoff: upward-step overshoot is 29% for Adam versus 20% for Gauss–Newton.

Valve B reverses the ranking. Gauss–Newton reaches 6.71 degrees RMSE from 7.25 degrees initially. Adam passes through a similarly good controller, then drifts to 7.46 degrees—worse than the starting point. Coordinate-wise normalization gives a small, consistently signed gradient component disproportionate influence; momentum pushes the trajectory farther. Sign-only updates help isolate normalization as a cause, rather than attributing everything to momentum.

What simulation cannot settle

The twins reveal the friction mechanism but fail to predict which optimizer wins on a particular unit. Valve B's twin even reverses the hardware ranking of the tuned controllers. Cross-validation simulation errors reach 4.9–13.9 degrees, and some physical parameters are only partially identifiable.

The hardware evidence is limited to two valves and a few tuning runs per method. No gradient-free optimizer is benchmarked. The practical lesson is narrower than choosing Adam or rejecting it: design experiments around the intended operating range, inspect gradient reliability, and use separate validation to stop tuning before apparent progress becomes drift.