A putative new idea for AI control; index here.

Previously, I presented a model in which a “rationality module” kept track of two things: how well a human was maximising their actual reward, and whether their preferences had been overridden by AI action.

The second didn’t integrate well into the first, and was tracked by a clunky extra Boolean. Since the two didn’t fit together, I was going to separate the two concepts, especially since the Boolean felt a bit too... Boolean, not allowing for grading. But then I realised that they actually fit together completely naturally, without the need for arbitrary Booleans or other tricks.

Feast or heroin famine

Consider the situation detailed in the following figure. An AI has the opportunity to surreptitiously inject someone with heroin ($I$) or not do so ($\neg I$). If it doesn’t, the human will choose to enjoy a massive feast ($F$); if it does, the human will instead choose more heroin ($H$).

So the human policy is given by $\pi \left(I\right)=H,\pi \left(\neg I\right)=F$. The human rationality and reward are given by a pair $(m,R)$, where $R$ is the human reward and $m$ measures their rationality - how closely their actions conform with their reward.

The module $m$ can be seen as a map from rewards to policies (or, since policies are maps from histories to actions, m can be seen as mapping histories and rewards to actions). The pair $(m,R)$ are said to be compatible if $m\left(R\right)=\pi$, the human policy.

There are three natural $R$s to consider here: $R_p$, a generic pleasure. Next, $R_e$, the ‘enjoyment’ reward, where enjoyment is pleasure endorsed as ‘genuine’ by common judgement. Assume that $R_p\left(H\right)=1$, $R_p\left(F\right)=1/3$, $R_e\left(F\right)=1/2$, and $R_e\left(H\right)=0$. Finally, there is the twisted reward $R_t$, which is $R_p$ conditional on $I$ and $R_e$

There are two natural $m$s: $m_r$, the fully rational module. And $m_f$, the module that is fully rational conditional on $I$, but always maps to $H$ if $I$ is chosen: $m\left(R\right)\left(I\right)=H$, for all $R$.

The pair $m_r\left(R_e\right)$ is not compatible with $\pi$: it predicts that the human would take action $F$ following $I$ (feast following injection). The reward $R_p$ is compatible with neither $m$: it predicts $H$ following $\neg I$ (heroin following no injection).

The other three pairs are compatible: $m_r\left(R_t\right)$, $m_f\left(R_t\right)$, and $m_f\left(R_e\right)$ all give the correct policy $\pi$.

Overriding rewards and regret

This leads to a definition of when the AI is overriding human rewards. Given a pair $(m,R)$, with $m\left(R\right)=\pi$, and AI’s action $A$ overrides the human reward if $\pi |A$ is poorly optimised for maximising $R$. If $V^{\pi }\left(R|A\right)$ is the expected reward (according to $R$) of the actual human policy, and $V^{\ast }\left(R|A\right)$ is the expected reward (according to $R$) of the human following the ideal policy for maximising $R$, then a measure of how much the AI is overriding rewards is the regret:

$V^{\ast }\left(R|A\right)-V^{\pi }\left(R|A\right)$.

One might object that this isn’t the AI overriding the reward, but reducing human rationality. But these two facets are related: $\pi |A$ is poorly fitted for maximising $R$, but there’s certainly another reward $R^{\prime }$ which $\pi |A$ is better suited to maximise. So the AI is forcing the human into maximising a different reward.

There’s also the issue that humans are poorly rational to start off with, so we have large regret for AIs that don’t do anything; but this makes sense. An AI that established our reward $R$ and didn’t intervene as we flailed and failed to maximise it, wouldn’t be a success in its role.

(An alternate, but related, measure of whether people’s reward is being overridden is whether, conditional on $A$, $m\left(R\right)$ is ‘sensitive’ to the reward $R$. A merely incompetent human would have $m\left(R\right)$ changing a lot dependent on $R$ - though never maximising it very well - while one with reward overridden would have the same behaviour whatever $R$ it was supposedly supposed to maximise).

Back to the example above. The $(m_r,R_t)$ pair means that the human is rationally maximising the twisted reward $R_t$. The $(m_f,R_t)$ is one where the injection forces the human into a very specific behaviour - specific behaviour that coincidentally is exactly the right thing for their reward. Finally, $(m_f,R_e)$ claims that the injection forces the human into specific behaviour that is detrimental to their reward. In the first two cases, the AI’s recommended action is $I$ (expected reward $1$ versus $1/2$ for $\neg I$), in the second it’s $\neg I$ (expected reward $1/2$ versus $0$ for $I$).

(Of course, it’s also possible to model humans are opiode-maximisers, whose rationality is overridden by not getting heroin injections; as already stated, rewards and rationality cannot be deduced from observations alone).

Hence the concept of overriding human preferences appears naturally and continuously within the formalism of rationality modules.