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TM009

Credit assignment problem

Also: credit assignment, blame assignment

In Spanish: Problema de asignación de crédito

The problem of distributing credit or blame for an outcome among the many decisions, steps, or parameters that contributed to it.

Marvin Minsky (1961) framed it with an example: if winning a chess game involves a million decisions, does each deserve one-millionth of the credit? He called it the basic credit assignment problem for systems that learn by reinforcement. It has two faces.

Structural: which part of the system. In a network with hidden layers, the error is observed at the output, but nobody says what the intermediate units should have done; deciding that amounts to deciding what they should represent (Rumelhart et al., 1986, p. 533). Around 1969 there were no effective rules for training more than two layers of adjustable weights (Buckner, 2024, p. 120). Backpropagation solved it for differentiable networks; M. Mitchell (2019) calls it, precisely, a credit-assignment algorithm (2019, ch. 5, n. 1).

Temporal: which moment. In reinforcement learning the reward comes late: which move decided the game? In M. Mitchell (2019)'s example, a robot learning to kick a ball must not conclude that a kick at empty air, far from the ball, was a necessary step toward the reward: that would be superstition. The value of actions propagates backward one step per episode (2019, ch. 8). Samuel's checkers program already compared a position's evaluation with the one obtained after exploring its continuation, the seed of temporal-difference learning (Sutton & Barto, 2018). In recurrent networks, backpropagation through time plays this role.

Today. In RLHF and in reasoning models, a single reward judges a response thousands of tokens long: distributing it is the same problem at another scale.

A philosophical angle. This is a technical version of attributing causal responsibility when many hands are involved. Neuroscience offers a parallel: dopamine signals reward prediction errors (Buckner, 2024, p. 169, n. 15), like the temporal-difference error. But neurons do not seem able to send error signals backward across the synapse, and how the brain solves the structural part remains under debate (2024, p. 132, n. 11).

Sources

  • Buckner, C. J. (2024). From deep learning to rational machines: What the history of philosophy can teach us about the future of artificial intelligence. Oxford University Press. https://doi.org/10.1093/oso/9780197653302.001.0001 §
  • Minsky, M., & Papert, S. (1969). Perceptrons: An introduction to computational geometry. MIT Press. §
  • Mitchell, M. (2019). Artificial intelligence: A guide for thinking humans. Pelican Books. §
  • Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature, 323(6088), 533–536. https://doi.org/10.1038/323533a0 §
  • Sutton, R. S., & Barto, A. G. (2018). Reinforcement learning: An introduction (2nd ed.). MIT Press. §