I don’t currently know of any example where this achieves better performance than LIDT. The raw action-expectations of the logical inductor, used as an embedder, will always pass the reality filter and the CDT=EDT filter. Any embedder differing from those expectations would have to differ on the expected utility of an action other than the one it recommended, in order to pass the CDT=EDT filter. So the expected utility of alternate embedders, according to the those embedders themselves, can only be lower than that of the LIDT-like embedder.
There seems to be a deep connection between the CDT=EDT assumption and LIDT-like reasoning. In the Bayes-net setting where I prove CDT=EDT, I assume self-knowledge of mixed strategy (aka mixed-strategy ratifiability) and I assume one can implement randomized strategies without interference (mixed-strategy implementability). LIDT has the first property, since a logical inductor will learn a calibrated estimate of the action probabilities in a given situation. In problems where the environment is entangled with the randomization the agent uses, like troll bridge, LIDT can do quite poorly. Part of the original attraction of the CDT=EDT philosophy for me was the way it seems to capture how logical induction naturally wants to think about things.
I don’t think loss relative to the argmax agent for the true environment is a very good optimality notion. It is only helpful in so far as the argmax strategy on the true environment is the best you can do. Other agents may perform better, in general. For example, argmax behaviour will 2-box in Newcomb so long as the predictor can’t predict the agent’s exploration. (Say, if the predictor is predicting you with your same logical inductor.) Loss relative to other agents more generally (like in the original ADT write-up) seems more relevant.
I don’t currently know of any example where this achieves better performance than LIDT. The raw action-expectations of the logical inductor, used as an embedder, will always pass the reality filter and the CDT=EDT filter. Any embedder differing from those expectations would have to differ on the expected utility of an action other than the one it recommended, in order to pass the CDT=EDT filter. So the expected utility of alternate embedders, according to the those embedders themselves, can only be lower than that of the LIDT-like embedder.
There seems to be a deep connection between the CDT=EDT assumption and LIDT-like reasoning. In the Bayes-net setting where I prove CDT=EDT, I assume self-knowledge of mixed strategy (aka mixed-strategy ratifiability) and I assume one can implement randomized strategies without interference (mixed-strategy implementability). LIDT has the first property, since a logical inductor will learn a calibrated estimate of the action probabilities in a given situation. In problems where the environment is entangled with the randomization the agent uses, like troll bridge, LIDT can do quite poorly. Part of the original attraction of the CDT=EDT philosophy for me was the way it seems to capture how logical induction naturally wants to think about things.
I don’t think loss relative to the argmax agent for the true environment is a very good optimality notion. It is only helpful in so far as the argmax strategy on the true environment is the best you can do. Other agents may perform better, in general. For example, argmax behaviour will 2-box in Newcomb so long as the predictor can’t predict the agent’s exploration. (Say, if the predictor is predicting you with your same logical inductor.) Loss relative to other agents more generally (like in the original ADT write-up) seems more relevant.