Gradient descent and random search as baselines for gene-network behaviour optimisation

Friston, Daunizeau and Kiebel (2009) noted that minimising free energy could use a stochastic search, sampling the sensorium randomly for a percept with low free energy. They chose to focus on gradient descent¹. Friston and Ao (2012) assumed that minimising free energy over action and internal states conforms to a generalised gradient descent². Calvo and Friston (2017) described the minimisation of surprise in dynamical systems as, at its simplest, a gradient descent. They applied the idea to plants³. Here the descent is a model of how a system behaves, not a method used to design one.

Kriegman, Cheney and Bongard (2018) described the Hinton and Nowlan model, in which a bitstring has value only when it matches a target exactly. The search space has a single spike of high fitness with no slope, and evolution there is no better than random search⁴. In their own robot experiments, the highest mutation rate made optimisation of the non-developmental morphologies reduce to random search. The two best treatments had development, and their robots were significantly faster than those from random search⁵.

Blackiston, Kriegman, Bongard and Levin (2023) reviewed xenobot design by simulation. Searching in simulation filtered out billions of bad designs before any were built. This greatly improved efficiency in the wetlab and reduced biowaste. They also said the process is energy-intensive and that its carbon footprint grows with simulation time. They called this arguably the most pressing ethical concern of xenobot research. They proposed encoding the design space so that gradients can be followed instead of meandering through random variants. They suggested that, if successful, this could cut processing time by several orders of magnitude⁶.

Etcheverry, Moulin-Frier, Oudeyer and Levin (2025) took up an oscillator engineering task from Hiscock (2019). Parameters of a gene circuit model are tuned to give oscillation with a target amplitude, frequency and offset. They compared random search, gradient descent, an evolutionary algorithm and their curiosity search, each with a budget of N=5000⁷. The gradient descent baseline used a mean square error loss between the phenotype node activation and a cosine target. It used the Adam optimizer from a random starting parameter, with the same number of model rollouts as the other methods⁸.